Daniela Berti

Environmental conflicts and the Judicialization of Nature in India a

The aim of this paper is to show how questions related to the environment and religion may sometimes overlap in Indian judiciary practice. Courts in India are sometimes called upon to make a ruling about writ petitions which involve promoters of public works (hydroelectric projects, dams, tourist resorts, etc.) whom villagers accuse of not only spoiling a natural environment but of damaging a place where a village god allegedly lives. I discuss one example of these writ petitions that I followed up during my fieldwork at Himachal Pradesh High Court in Shimla. The case concerns the building of a water tank near a natural source supposedly inhabited by jogni (powerful feminine beings). Based on ethnographic material and court files, the paper shows how nature is presented in these petitions both in ecological terms, as a resource with an intrinsic value that has to be regulated by law, and in terms of a place over which gods have specific rights.

Recent studies on development projects and the management of natural resources in different regions of the world have highlighted the increasingly important role played by the courts in cases involving environmental protection. This trend has often been presented as the result of a judicialisation of politics, a process that Hirschl (2006: 721) defines as the "ever-accelerating reliance on courts and judicial means for addressing core moral predicaments, public policy questions, and political controversies". In political sociology this process has been interpreted as an extension of the jurisdiction of the court at the expense of politicians or the administration (Commaille et al. 2010; Commaille and Kaluszynski 2007). Couso et al. (2010), for example, showed how judges in Latin America have begun to take on the role of human rights defenders in recent years. The result is that today crucial political issues, such as conservation and resource management, take on legal forms. But use of the law to define the relationships that people have with their natural environment does not come only from the milieus of professional. Indigenist movements, as well as individual farmers, sometimes supported by non-government organizations, often turn to the courts to oppose projects put forward or approved by the government, that they consider as endanger-/p. 112/ ing their livelihoods or depriving them of rights they previously enjoyed (Sieder 2010).

This judicialisation of environmental disputes takes on special importance in India, due in part to the relative ease with which villagers can go directly to courts of appeal (especially the High Court) through writ petitions (requests for assignment). Numerous cases are pending at the country's High Courts, sometimes for a number of years, which has led to the introduction of Green Benches in several High Courts and the creation in 2010 of a National Green Tribunal. This process, which in India was 'driven by judges' (Amirante 2012), has also been facilitated by the introduction in 1979 of the process of Public Interest Litigation (PIL), by which a member of the 'public' may plead to the High Court or the Supreme Court against the violation of a constitutional right, even though the person is not necessarily a direct party to the case. This procedural innovation has permitted, on the one hand, the development of judicial activism, whereby judges can take the initiative and thus become defenders and promoters of environmental or ecological values, and on the other hand, has also allowed the economically disadvantaged to seek justice, merely by writing a single letter, and oppose practices or projects affecting public interest. An example frequently cited in judicial circles in Himachal Pradesh, for example, is the case of Kinkri Devi, an illiterate peasant woman from an isolated village in the mountains, who had submitted a PIL to the High Court in that State in 1987, denouncing the harmful effects of illegal mining on the environment. Her action, supported by a local environmental organization, was well covered in the national and international press and contributed to the introduction of a number of measures to address the problem.

Although in most cases the arguments put before the court refer to modern concepts such as ecology, sustainable management of natural resources, environmental protection, and a scientific approach to nature, in some cases these discourses have been mixed in with religious arguments. As noted by Tomalin (2004: 287), one area where religion has joined the environmental debate is in the Hindutva (Hindu right-wing fundamentalist) movement. One example is the longstanding campaign against the Tehri dam, in what today is Uttarakhand, where the religious arguments used by environmental activiststhat the building of a dam on the headwaters of the river Ganga would disturb the Ganges (goddess) self-purification powershas been reinterpreted according to the rhetoric used by Hindutva leaders active in the region, who are more concerned with the discourse about the Ganges as a symbol of Hindu culture and nation. 1 However, this mutual association between religion and ecology does not always take a Hindutva turn. In the pages that follow, I rely on historical and /p. 113/ ethnographic material for the region of Himachal Pradesh to analyze a context where the ecologist discourse is strongly related to the local cult of village gods. This is particularly the case in the context of environmental conflicts over territories where these gods are said to live. In the first part of this contribution I briefly present the ritual framework of village gods to show how, due to the power these gods are thought to have over natural events, they have been playing an institutional role in different historical and political contexts. I then show how today the idea of a natural landscape inhabited by village gods and goddesses is in keeping with the discourse put forward by ecology organizations. In the last part of the contribution I analyze a long-standing conflict between the promoters of a hydroelectric project that was to be built in a woodland area and the followers of a village goddess who was said to live there. The analysis of this case shows how the idea that emerges in the context of these village cults, that nature is controlled by village gods, merges with other contrasting ideas of nature, which partly reflect the ecologist discourse that confers a cultural value on nature and are also a consequence of the legal and judicial framework that villagers have to adhere to in such litigations. On the other hand, the religious discourse that was put forward more vehemently by the local population as the main reason for their opposition to the project also appears to be due to villagers' concerns over the management of natural resources.

Ruling with nature

The idea that the landscape is inhabited by gods and goddesses who have the power to influence 'natural events', bringing rain or sunshine, a good harvest or famine, has been central to the form of governance adopted in different Himalayan kingdoms as well as in other parts of India. For the region concerned, which corresponds to today's district of Kullu in Himachal Pradesh, royal documents dating back to the seventeenth century reveal how local kings adopted a royal model that was common to many Hindu kingdoms and in which the king was portrayed as a delegate or servant (gulāmī) of a state deity on behalf of whom he ruled.2 This way of legitimizing the king's power in the figure of a state god goes hand in handin Kullu as in other Himalayan kingdoms -with the king's acknowledgment and subordination of village deities who were honoured at local level. 3 While the royal deity confers legitimacy on the ruler, village deities are said to control natural resources within the kingdom. Oral accounts collected by Emerson (n.d.), a British administrator who governed the region of Shimla during the colonial period, attest to how a village deity satisfied the raja's request to bring rain in a period of drought, and how the raja rewarded the de-/p. 114/ ity in various waysby giving land or honours, or building a temple or a palan-quin. 4 Emerson's records also recount how the raja could exercise 'pressure' on village deities and on the powers (śakti) they were considered to have over natural events. It is said for instance that in times of drought, the raja used to summon all deities' mediums to his palace and to ask all the deities to bring rainand if rain did not come at once, he threatened to have their heads cut off (ibidem). When the region fell under colonial control, the British administrator could also be asked on occasion to assume a royal role and to intervene in these matters. Emerson reports an instance of such a request where he himself became involved in issues regarding local gods. When governing the region of Shimla, shortly after the East Indian Company had assumed ultimate authority over it, he received the visit of some villagers one day. They came to ask him to punish the mediums of a very famous god in the region, Kamru Nag, who was considered to be responsible for the shortage of rain. Emerson in fact decided to play along with the game. His manuscript reads:

It was clearly up to me to do something, and as all arguments failed to convince the people, I finally gave orders to the Wazir [minister of a territory] to call the erring diviners, I took the opportunity of reminding them of their duties, and the punishments prescribed for their neglect. They were refreshingly candid. Kamru Nag's job, they admitted, was to send sunshine and rain in their proper season. If he failed to do so, they (the diviners) were called to the police station and kept confined. If the rain did not then come within a reasonable time, they were made to stand naked in the sun; or if fine weather was needed and rain fell, they were made to stand up to their waists in the river until the sun shone. They knew of no reason why the same measures should not now be taken, but they would like four days of grace, and if no rain came within that time, they would bow to whatever punishment was ordered. So they were given their four days, and as rain fell before they ended, no further action was necessary. (ibidem)

The raja's role in consulting the gods about natural events is perpetuated today by the descendent of the Kullu royal family, Maheshwar Singh who, like other rajas in the region, is also a politician. His political role often merges with the ritual role he plays as raja. 6 As the private owner of the royal temple, which is part of the ancient royal palace where he still lives, he continues to be recognised as a 'servant' of the royal god and to celebrate the Dashera festival /p. 115/ in this god's honour (Berti 2009b). He also continues to assume the role of 'mukhya kardār' (chief administrator) of village deities, though the ritual relationship he now has with village gods is often portrayed by his political opponents as a way of creating political alliances with the gods' followers. (Fig. 1) 6 As member of the BJP (Hindu right-wind party), Mahesvar Singh had been an elected member of the Lokh Sabha in the past, though he has now left the BJP to create his own party. In the 2004 elections Mahesvar Singh was defeated by a member of another royal family, Rani Pratibha Singh, the wife of the current Chief Minister of Himachal Pradesh, Virbhadra Singh, who is the descendant of the Bushahar royal family, a kingdom that is nowadays part of Shimla district. On the role that rajas may have in contemporary politics see also Hurtig 1988 and Price 1996. In August 1999 Maheshwar Singh decided to renovate the Jagti Patt temple in Nagar, an ancient royal capital, where his ancestors are thought to have held large-scale consultations with the gods. At the entrance to the temple a notice board explains the origin of the place to visitors in English:

Even now during the great hour of natural calamities, other miseries … all the representatives of god and goddess gur pujar, etc. carrying the insignia of their devi […] assemble at this holy place. Head of the Kullu raj family with the order of devi-devta organize the function with traditional reverence. […] Since renovation of the Jagti Patt temple, Maheshwar Singh has occasionally organized large-scale public consultations of village gods and goddesses, inviting them to Nagar with their mediums and their mobile icons. One ex-ample is a case that concerns a Himalayan Ski Village development project in the Kullu district of Himachal Pradesh, which had been put forward by the heir of the Ford family. The project was first discussed during temple consultations organized at village level (deopūchnā) when people go to consult the local deity through his or her medium. Some main deities from the region /p. 116/ were said to have expressed their opposition to the project, arguing that it would spoil the places where they live. In 2006, raja Maheswar Singh who, as a politician, was opposed to the project, decided to organize a large-scale jagti pūch (also called dev sansad, the parliament of gods) at Nagar temple. He gathered together the mediums of various deities of the region and asked them to express their opinion. As an article in Frontline reports, (in the jagti pūch) the gods and goddesses 'unanimously vetoed the proposal'.7 (Fig. 2) God after god spoke and made it clear that they did not want the ski village in the area since it would desecrate holy places. They warned the people that if the project was approved, the gods would leave and destroy the area. 8 While the media presented the gods as real actors in the controversy, they also referred to the political implications. An article published in Frontline (8-21 /p. 117/ Apr 2006) noted how 'The mobilisation of the gods has proved to be an effective subversive strategy for the opposition, the Bharatiya Janata Party'. Another article published in Outlook argued that as Maheswar Singh is also a politician, a former MP from the BJP party, 'his involvement in the 'devata ' [deities] controversy lends credence to allegations that the state unit of the party is trying to scuttle the project with the help of the gods. Incidentally, the devatas have also 'instructed' Maheshwar to invite CM [Chief Minister] Virbhadra Singh to the assembly so that "he can see and hear for himself the divine objections".9

Both sides of the discourse -the gods' intention and people's strategyare particularly evoked when the case submitted to the deity is a matter of public interest. In fact, given the power these deities are considered to have over natural events, they continue to play a role in the public sphere not only at village level but also at state level, especially in the context of jagti pūch, where they may operate as counter powers or as an arena for contesting government decisions.

The 'green' twist

Today, the idea of a landscape inhabited and controlled by village gods may clash with the state's development policy which advocates the implementation of projects involving construction works on a territory where a god is supposed to live. One of the issues brought up during ritual consultations, when villagers address their gods through their institutional mediums, is nature conservation. The 'environmental issue' is more and more widespread among people living in rural areas, including within the gods' closest entourage. Newspapers often focus on this point in their headlines. In the case of the Himalayan ski project mentioned above, an article reports on how the project 'had come unstuck after a group of Hindu gods ruled that it was environmentally unsound'. 10 Another article reports that the medium of Jamlu, a famous god in the region who had expressed his opposition to the project, when interviewed by the journalistthus speaking for himself -had said that 'the ski resort would have polluted their water and that the gods did not want their land to be violated.' 11 The environmental issue is also put forward by gods' followers regarding the recent practice attested to in various Himalayan regions of India to create 'god's protected forests'. Aggarwal (2010: 35) reports how in the nearby region of Kumaon, which corresponds to the state of Uttarakhand today, these /p. 118/ areas (called dev arpit panchāyat forests, that is 'forests under god's protection') have been set up after a decision taken by village councils (panchāyat) to regenerate degraded woodland.

The communities retain some patches of forest to meet their requirements and on a designated date they visit the temple of a nearby deity and submit a letter of intent to the deity [mentioning] the area to be dedicated and the period of dedication. (ibidem)

The author points out that these 'protected areas' are not to be confused historically with older areas commonly called 'gods' forests' (dev van) which are also considered to be under the gods' control but which came into existence centuries ago as a consequence of royal donations. Unlike dev arpit panchāyat forests, these dev van did not stem from an environmental concern even though, as the author notes, 'implicit rules of use associated with these groves may sometimes coincide with those of the dev arpit panchāyat forest'. 12 However, the fact that these two kinds of gods' forests are sometimes confounded is shown, for instance, in the discourse held by environmental protection organizations which tend to present these dev van as proof of 'primitive ecological wisdom' (Milton, quoted in Tomalin 2004: 268). 13 A 11 "Fords Vs The Icons", see note 9. 12 Freeman's research on sacred groves (kavus) in Kerala suggests that sacred groves have always taken a variety of forms that do not necessarily coincide with the modern environmentalist's idea of 'pristine relics from a primeval past' (Freeman 1994:11). See also Tarabout in this volume. 13 Tomalin (2004) has shown how this religious environmentalism rhetoric, according to which In-dia has a long tradition of caring for nature, which has only clear example of this rhetoric is to be found on the WWF website for Himachal Pradesh where a specific section is dedicated to the socalled 'Sacred Groves' defined as 'a repository of floral and faunal wealth' and therefore as 'a major component of environmental protection'. The section reads:

The concept seems to have emerged in traditional societies where people attached sacredness to various species. Unknowingly, such traditional and cultural attitudes have made a significant contribution towards conserving these plant species. In Himachal Pradesh, the local myths and legends associated with sacred groves go a long way in preserving the forests from destruction. 14 Here the notion of nature is also linked to the idea of 'tradition' and 'cultural heritage'an association which is frequently made with environmental issues in other parts of the world (Siniscalchi 2007). Another part of the WWF website reads:

It has hence become imperative to restore the cultural and natural heritage of the Himalayas. It is in this regard that a three year project, 'Documentation of sacred and protected groves of Himachal Pradesh and their woody flora' was undertaken. ("Sacred Groves", see note 14).

/p. 119/

Another example is to be found in a brochure entitled 'A study of the Socioeconomic and Environmental Implications of the Reṇukā Dam Project' published by a regionally based NGO in 2010 and where 'ecological values and the landscape' are presented as 'closely intertwined with the spiritual and religious ethos of mountain societies'. The brochure also reports on how Lake Reṇukā, which would be affected by the dam project, is presented in the legend as 'a small pond into which Reṇukā, an incarnation of Goddess Durgā […] jumped in after she was abducted by a king who wanted to marry her', recently been broken due to Western influences of colonialism and consumerism is a simplistic analysis. See also Baviskar 1999:24. 14 "Sacred Groves", http://www.wwfindia.org/who_we_are/where_we_work/state_offices/hi-machal_pradesh /?5821/Sacred-Groves. and these stories are presented as an essential part of the religious life of people in the area. Another case reported in the brochure is that of Mahāsū, a well-known god in the region for the control he supposedly has over the rain. The above-mentioned website states that the place where Mahāsū lives will be flooded if the dam is built and therefore villagers believe that 'there will be divine intervention whenever the dam authorities will try to force them out".

In the cases mentioned above, the arguments put forward by ecologists on the one hand and by the gods' entourage on the other appear to be consistent with each other, as both groups were opposed to the project. In other cases, however, the environmental issue appears to be strongly opposed to the arguments presented by the god's followers. This is particularly true in projects related to national parks where the idea of creating a 'repository of savage fauna' may be associated with ridding the area of all human presence. One example of this is the Great Himalayan National Park, where the project of creating a 'wildlife sanctuary' included the relocation of the populations living in the area concerned and who used forest resources in accordance with the gods' rules. 15 Here, the will to preserve a natural place clashes with the will to follow the rules laid down by the god who supposedly inhabits the area. In a documentary produced by Barnela, which is significantly entitled 'Devta Activists', these positions appear to be incompatible. 16 In the documentary, the president (pradhān) of one village situated within the park's perimeter explains how since 1999, when their dwelling-place was declared part of the Great Himalayan National Park, the order given by the god through his medium to protect the forest, which consisted in using the resources only during a specific limited period for grazing and grass collection, clashed with park rules to forbid any access to the forest. One man from the same village explains:

I told the devtā [god] that the national park officers are preventing us from entering the area. The devtā said 'don't worry, I am here for you. … The forest belongs to me. No /p. 120/ one can stop you from entering.

[…] I will use my power to put pressure on the government. (Syncline Films) Some of the villagers interviewed in the documentary also point out the contradiction in government officials' attitudes who, after preventing them from entering the park, agreed to the construction of a hydro-electric power project within the park's protected area. As the documentary shows, the gods' mediums expressed the gods' dissatisfaction with the project, this time demanding on their own behalf that the natural site be protected, and threatening to leave the place if work was not stopped. And as one medium said, speaking as if he were the god 'I (the god) cannot tolerate this change in landscape. My power is leaving me. I am nothing more than a toy' (ibidem).

In the case of the Great Himalayan National Park, this tension between nature protection and development policy has to be understood whilst taking into consideration complex local and national political interests as well as the discourse held by the many actors involved in or affected by the creation of the parkpoliticians, park directors/officials, villagers, gods' mediums. (cf. Baviskar 2003, and Saberwal & Chhatre 2001). For the purpose of the present contribution, the case of the National Park shows that, while in some cases the idea of god-controlled nature may readily concur with the ecologist argument, with gods' mediums becoming the main supporters of nature conservation, in other cases it may prove to be the main argument that prompts villagers, with their gods, to oppose the way an environmental protection policy is implemented.

The 'Joginī case'

In July 2006 Water Miller, a private energy and water supplier, signed an agreement with the state of Himachal Pradesh to set up a 1 megawatt Hydro Electric Project in the forest near the village of Vashist, in the Kullu valley. For several years the project only existed on paper but in 2011 construction work started. Pneumatic drills were used and a pipeline was installed that ran along the ground. However, as soon as the project had been announced, the in-habitants of the area started to protest, and notably the people of Vashist, the village closest to the place selected by the Water Miller Company, who said that the work would damage the forest where the goddess Joginī supposedly lived. 17 The goddess's presence in this place is associated with a huge waterfall situated in a mountainous forest environment on the edge of the village. A /p. 121/ footprint on a stone (padam) near the waterfall is supposed to represent the goddess's first step upon her arrival there. There is also a small shrine where people from Vashist and from more remote villages used to come to perform the first hair-cutting ceremony (muṇdan). (Fig. 3) Fig. 3. The 'Jogini fall' 17 In the region, the term jognī is commonly used by gods' followers to indicate an undefined category of powerful feminine beings who are supposed to live in natural places such as trees, rivers, forests, waterfalls. Compared to other jognī of the area, Mahā Mai Joginī of Vashist has a more personalized identity. During ritual consultations, when people address the goddess through the medium to ask about their problems, the medium can tell that a jognī has taken possession of the person while he/she was walking in the forest and has made them sick. Berti, 2001. At village level, discussions were first held within the context of temple consultations (deopūchnā, 'questioning the god') during which the village deity is addressed through the institutional medium. Various gods and goddesses of the area, who had been consulted on the issue, were said to have indeed expressed their disapproval of the project. In fact, although the construction work only directly concerned one particular areathe forest near Vashist villageit ended up involving a number of neighbouring villagers and deities who were ritually linked to the goddess Joginī. A large-scale consultation of the gods (jagti pūch) was scheduled, which made the newspaper headlines. An article appeared in The Times of India, for instance, announcing the project under the title "Appeal against hydel power project to be taken to deities parliament"the idea of parliament often being used for jagti pūch to underline the role that gods are supposed to play as decision makers. 18 The article reports on how the people of Kullu 'after trying both requests and /p. 122/ protests against a hydro-electric project […] are planning to call on 'Jagti', the parliament of deities, to save the shrine of goddess Joginī (ibidem).

The goddess's followers also demonstrated in the street, accusing the construction workers of 'destroy[ing] the stone foot-print (padan) and […of…] desecrate[ing] the piṇdī (offerings) made in her honour'. Religious arguments were presented along with the environmental issues. An article in The Tribune reported:

The villagers said the setting up of such a project would cause ecological imbalance and environmental degradation. It will also hurt the religious sentiments of the devotees who come to pay obeisance to Goddess Jogini at the Jogini waterfall. 19 The issue of 'cultural heritage' was also brought to the fore. Villagers asked the government to impose an 'Environment Impact Assessment' on the Water Miller Company in view of recognizing the site as a 'pilgrimage spot' (The Tribune, 27 July 2011). They also requested that the place be declared a 'ecosensitive sacred site' (ibidem). Interestingly, the institution to which they addressed their claims was the Department of Art and Language, an institution which had already promoted many aspects of local culture in the past. Like other situations that rally support for environmental issues, here nature is attributed a cultural value and presented as a 'common good' that must be transmitted and protected (cf. Audrerie quoted in Siniscalchi 2007).

The mobilization took on a political dimension. In the early stages of the protests in 2009, the inhabitants of Vashist village and of other neighbouring villages had threatened to boycott the forthcoming general elections in order to force the government to abandon the project. They had prevented political leaders from organizing their electoral campaign in the village unless construction work was stopped. A number of meetings and demonstrations were organized in the street. (Fig. 4)

Village women along with women's organizations took part in the protests, brandishing slogans about the special relationship women are supposed to have with the goddess Joginī (The Tribune, 2011). Local politicians were also very much involved in the protests and during their electoral speeches they did not fail to show their support to villagers and their active role in the mobilization. The article mentions for instance that: Kullu MLA Govind Thakur, also from BJP, led a delegation of residents to Shimla and apprised Chief Minister Prem Kumar Dhumal of the sanctity of the Jogni Fall. The Chief Minister reportedly assured them that the government respected their sentiments and would take appropriate action in this regard soon.20

/p. 123/

In September 2011, after months of tension and protests, the Himachal Pradesh Chief Minister asked the Deputy Commissioner to hold a public hearing (jan sunāī). On that occasion the Water Miller director presented himself and the members of his company as local people who 'have full faith in the Deities, including Maha Maya Jogni [and who] would not do anything which is contrary to our and to the religious faith of the villagers as alleged' (letter to Deputy Commissioner included in the Court file, 2011). He also informed the Deputy Commissioner that he 'had obtained the permission of Maha Maya Jogni through its Gur [goddess's medium] late Sh. Mine Ram, in the year 2002 at the time of applying of the project' (ibidem). On the same occasion, he also asked the pujari to perform a puja for the goddess at her temple. In spite of the attempts made by the director to deny villagers' accusations, the protests continued. Three police FIRs (First Information Reports) were registered regarding the issue. In July 2011 a case was registered by the police on behalf of the Vashist temple administrator against the director of the company under section 295 of the Indian Penal code which pertains to 'injuring or defiling [a] place of worship with intent to insult the religion of any class'. Some weeks later, another case was registered against him at the police station, this time by three Vashist women who accused him of sexual harassment. According to the complaint, the manager of the Water Miller Power Company, Hari Babu, and four policemen allegedly "outraged their [the three women's] modesty by tearing their clothes and attempted to rape them when they were offering prayers at the holy Jogni fall." 21 However, on the very same day, a criminal case of 'assault on [a] public servant' was also registered by a constable and which contained a very different version of the 'rape story'. According to the guard, the manager, who had been told that villagers were intentionally damaging building materials, went to the project development site and was assaulted by a group of villagers who snatched his camera and mobile phone, and started beating him. They then asked three women to come from the village and forcibly made the manager and the guard sit among them while they took photographs, warning them that they would file a false rape case against them. 22 /p. 124/

This episode shows the various ways the court may be used; as a place to denounce an alleged case of abuse and at the same time as a weapon for getting the company's employees into trouble. This was at least the opinion of the company director who, as he put it while airing his views about the case, "Those who are called 'poor villagers' have become smart now." In addition to pestering the company, villagers continued to protest in the streets. In September 2011 a delegation of Vashist villagers, along with a local deputy, was received by the Chief Minister in Shimla 'to apprise him [the Chief Minister] of the sanctity of the Jogni Fall' 23 (The Tribune, 27 July 2011). A Vashist man, a member of the delegation described the event a year later:

We went to see him [the Chief Minister] in his office at Shimla and, you know, Joginī Mātā always told us that 'you go, you start the case and I will be with you.' When we went to his office we were 15 men and 15 women and as soon as the Dhumal [the then Chief Minister, from BJP] saw the women he said 'Look the joginī have come here!' Then he said that this project will never be built there, that he will give order to stop it. So we had seen clear that Joginī Mātā is with us because of this that words had come from his mouth. (Interview, Vashist 2012) 21 "Manager, four cops booked for rape bid." The Tribune, 4 August 2011. 22 http://kullupolice.blogspot.fr/2011/08/crime-report-dated-03082011-up-to-4-pm_04.html). 23 "Scrap Jogni Fall power project: Villagers Say the site is a pilgrimage spot" by Kuldeep Chauhan/TNS, The Tribune 28 July 2011.

In May 2012 the Chief Minister decided to ask the company to suspend work and to withdraw the government's agreement. The decision made the newspaper headlines: 'Project cancelled. Villagers jubilant'. 24 The Water Miller Company consequently decided to file a lawsuit.

When a writ petition was brought before Himachal Pradesh High Court, the arguments were presented on a legal register and according to a judicial procedure. The parties involved had to rally round to produce evidence and to present their arguments. First of all, to 'prove' that the goddess actually lived where the project was being developed, villagers provided the court with an official document in Urdu (the region was still part of Punjab), dated 1948, to certify that the then Secretary to the Government gave muāfi (property exempted from taxes) to the goddess. In another document in Hindi dated 1847, it is said that 'the goddess is the owner of the land and that villagers are tenants and they have either to serve the goddess or to pay a tax.' The forest in question is presented as the abode of the goddess Jogini and was exempted from payment of land revenue (Court file).

In the reply that the 'respondents' (that is Vashist villagers) gave to the writ petition, reference was made to the fact that the political authorities had shown their support. They mentioned the fact that: also the Hon'ble Chief Minister of H. P. had been kind enough to take a decision that the sentiments, customs and heritage of the local people will not be allowed to be /p. 125/ disturbed for the construction of this project. They [politicians] know it well that the water of these falls … has been preserved in its nature since generation to generation by the ancestors of the respondents and by custom as well as heritage they are totally devoted to the same.

The respondents also referred to the Constitution of India which protects 'the religious places of the citizens' andso they wroteno one is allowed to take over a place of cultural heritage, of natural importance, etc.

A second major point that emerges from the court file concerns reference to the notion of heritage and the link between the goddess's presence in the place and the 'heritage issue'.

'It being a place of heritage and religion, therefore, the area in question cannot be allowed to be encroached upon and grabbed by the petitioner Company. No one is permitted to reach the place of the first fall except at the time of special permission when certain religious ceremonies are performed. The second water fall is on the lower site where various religious functions take place throughout the years. The Mundan ceremonies of babies take place throughout the year.' (Court file, respondents' reply).

It is also mentioned in the file that:

The petitioner Company started construction work of water tank at the most sacred place of Maha Mai Jogni which is commonly known as "Narol" and in this process […] they not only caused extensive damage to the footprints of Maha Mai Jogni but also they damaged and destroyed the Pindi of Maha Mai Jogni about which a complaint (FIR) was lodged in police station. (ibidem) Along with the religious-ecology-heritage issue, the arguments presented to the court also revealed the economic interests that lay behind the conflict: for instance, Vashist villagers' opposition to the diversion of one of the waterfalls as stipulated in the construction project; the fact that, they would have lost their right to natural resources.

[The villagers of Vashist], … are the right holders with respect to the affected area, Jogini falls vis-à-vis drinking water, water for irrigations, religious rights, grazing rights, forest rights, etc. Reference was also made by the respondents to more technical points: that 'the company didn't ask for land demarcation of the area'; that the company 'did not ask for the "non objection certificate", to the panchāyat within which the area of Mahā Mai Joginī is falling' (ibidem). They even raised the question about the presence in the forest of wildlife and consequently of the company's violation of wildlife protection.

The case is still pending. I was told by one of the lawyers who are following the case that each time a date is fixed for the hearing the case is postponed.

/p. 126/

According to him the Water Mill Company has abandoned the project but is trying to obtain compensation from the state. However, independent of the court's final verdict, the case shows how the idea expressed by the god's followers, that nature is governed by village deities, has been integrated into contemporary state institutions of power and decision-making. On the one hand, the case shows how, in order to assert what they consider to be the gods' decisions, gods' followers have to rally around on multiple fronts and use diverse strategies: organizing street protests, attending meetings with politicians, talking to journalists, and preparing (or fabricating) evidence or arguments for the police or for the court. On the other hand, it also shows that more 'secular' protagonists of the casepoliticians, company directors, judgesare not only called upon to publicly take a stance regarding the gods' issue but also, particularly in the case of politicians, that they may eventually decide to back the gods' cause.

Conclusion

The role that religion and rituals may play in contesting or challenging certain development projects has been widely discussed in anthropological literature. Peterson (2006), for instance, in his work on the Republic of Congo, has analyzed a case-study similar to the Jogini case presented here, where villagers opposed a small-scale hydroelectric project by evoking the presence of Mata Wata, a goddess who is said to live in the area and to control the water resources. However, as Peterson shows, in this case the cult of this goddess had recently developed as a form of mobilization, with the main intention of opposing the project, whereas in the context presented in this article, the role that village gods are considered to play in the management of natural re-sources appears to be historically entrenched in the religious-political history of the region. Not only are gods considered by their followers to be the protagonists of the protests here but also, as in the case of the Himalayan ski re-sort mentioned above, pre-colonial forms of ritual relationships, such as those between the raja and the gods, continue to have a role to play in contemporary state policy. This is particularly true in cases where politicians are the descendants of royal families and, as in the case of Maheshwar Singh, they try to combine their ritual role as raja with their political career. However, even political leaders who are not of royal descent may attempt to play the role of supporter of the gods' cause, especially during electoral campaigns and in cases which prompt large-scale mobilization. 25 We have seen in the Jogini case presented above how MLA Govinda Thakur, from the BJP party, presented himself as a supporter of the cause launched by the goddess' devotees in a case where Maheswar Singh, on the contrary, was trying to convince them to al-/p. 127/ low the project to go ahead. But politicians from the Congress Party may also be fully taken up with what some people compare to the system of vote banks, with gods defined as 'BJP devtā' and 'Congress devtā'. (Berti 2009a).

The material presented here shows that not only do politicians running for elections take part in the 'gods' presence/activism' in public and political life but many other institutional and public figures, such as Deputy Commissioners, directors of Academies, journalists, green activists, police officers, judges may also be called upon occasionally to assume an important role in taking decisions regarding these cases. The various actors in these conflicts may have different motivations. On the one hand, the involvement of the king or of other politicians in their support of the gods may partly be interpreted, as newspapers often underline, in terms of their electoral stakes, which does not exclude their emotional involvement with the local gods. On the other hand, the struggle of gods' followers to defend what they present as the gods' instructions is frequently associatedboth in newspapers, in the court file and in villagers' statementswith claims over the management of natural resources, of water rights, irrigation rights, grazing rights, forest rights.

While politicians are more likely to share the point of view of gods' supporters who put forward the idea of a 'god's agency' and even take part in gods' consultations as in the case of Maheshwar Singh, when the case is actually brought before the High Court the issue of a god's presence in the place, although still mentioned in the file, is presented according to a judicial vocabulary and is adjusted to correspond to a question of rights or to legal sections. Thus, for example, in the Joginī case, reference was made in the file to the goddess's land rights, which could be officially proved in court, and to the 'heritage value' of the goddess' place of worship, or to the elaborate ceremonies performed at her temple. By contrast, no reference was made to the fact that the gods themselves, through their mediums, were supposed to have vetoed the projecta point that was raised, as we have seen, in newspaper headlines. In fact, even in cases where, due to the juristic personality that gods have in India, a god is mentioned in the file as the main petitioner for the case, the question of his 'agency' through his medium is not considered to be an admissible argument in court. From a judicial point of view, judges do not have to ascertain the gods' alleged existence in a place but to determine, for instance in cases regarding a god's property, whether the god really owns the land or any other property, whenever this property is contested by another party.

Paradoxically, in cases where local deities are directly involved, religious questions may eventually be undermined by the court for the benefit of a more juridical reasoning, while in a number of cases where gods are not involved in the issue, judges do not hesitate to refer to religious ideas in their decisions. More specifically, if we take the issue of nature and environment /p. 128/ in a number of High-Court and Supreme-Court judgments, judges may dedicate pages and pages to quoting entire passages of Sanskrit religious or philosophical texts, sometimes punctuating these quotations with references to scientific or ecologist reasoning in an attempt to show how modern approaches to nature may already be found in ancient texts. We read, for example, in a judgment passed by a Supreme Court judge regarding an environmental protection case filed under the Forest Conservation Act concerning the mining of lime stone quarries in Dehradun:

Our ancestors knew that trees were friends of mankind and forests were necessary for human existence and civilization to thrive. It is these forests that provided shelter for the 'Rishies' and accommodated the ancient 'Gurukulas'. They too provided food and sport for our forefathers living in the State of Nature. That is why there is copious reference to forests in the Vedas and the ancient literature of ours. In ancient times trees were worshiped as gods and prayers for up-keep of forests were offered to the Divine. (Rural Litigation and Entitlement Kendra Vs. State of U. P., 1988) While religious references in some judicial decisions may derive from a judge's personal religious or ideological attitude, this kind of speculation re-mains rather abstract and does not really refer to arguments or ideas put forward by the parties in the case. By contrast, in cases such as the one presented here, where religious arguments are explicitly addressed at least by one of the parties, judges may prefer to focus on issues regarding rights and on legal sections without even considering the idea, so strongly evoked out of court, of a landscape inhabited and controlled by gods.

Fig. 1 .

 1 Fig. 1. Deity paying homage to Maheswar Singh during Dashera. (D. Berti, 2001).

Fig. 2 .

 2 Fig. 2. Maheswar Singh consulting deities' mediums at the jagti pūch (D. Berti).

8

  "Divine wrath could put ski resort deal on ice" by Vibha Varshney, Down to Earth, 15 March, 2006. http://www.downtoearth.org.in/node/7429 (26/11/2014).

Fig. 4 .

 4 Fig. 4. Demonstration against the project (M.C. Thakur)

  […] Our century old religious & other special rights have been ignored by influencing … the company. The company cannot play with our religious & traditional sentiments and their whims and fancies. (Court file, respondents' reply)

On the blurring of the boundaries between religious environmentalism and Hindu nationalism, see also Meera Nanda

2002[START_REF] Sharma | Passages from Nature to Nationalism: Sunderlal Bahuguna and Tehri Dam Opposition in Garhwal[END_REF][START_REF] Mawdsley | The abuse of religion and ecology: the Vishva Hindu Parishad and Tehri Dam[END_REF]

See Kulke 2001 and Schnepel 1994 for Orissa.

Cf. Vidal 1988 and Berti 2009b.

 4 The need to establish alliances with deities seems to have been a crucial element in the exercise of political power in all Himalayan kingdoms. By analyzing documents from the Kathmandu Valley, in Nepal,[START_REF] Burghart | Gifts to the gods: power, property and ceremonial in Nepal[END_REF] has shown how royal gifts of land to gods was one way for kings to establish personal alliances with them in order to obtain victory for themselves and prosperity for the kingdom.5 In his manuscript Emerson regards the gods as real 'actors' and describes the events in a somewhat narrative stylenot without some humour in order to maintain a certain distance.

"On thin ice", by Aman Sethi, Frontline, Volume 23, Issue 07, Apr. 08-21, 2006. http://www.frontline.in/static/html/fl2307/stories/20060421003310100.htm (26/11/2014).

"Fords Vs The Icons", by Chander Suta Dogra. Outlook, 6 February 2006. http://www.outlookindia.com/article/Ford-Vs-The-Icons/230097 (26/ 11/2014).

"Hindu gods turn down plans for a Himalayan ski resort", by Peter Fostr. The Telegraph, 21 February 2006: http://www.telegraph.co.uk/news/worldnews/asia/india/1511074/Hindu-gods-turndownplans-for-a-Himalayan-ski-resort.htm (5/05/2015).

http://www.greathimalayannationalpark.com/about-the-park-overview/index.html.

'Devta Activists', Sanjay Barnela, The Public Service Broadcasting Trust, Delhi, 2006. https:// www.youtube.com/watch?v=zt_9eB9UCl4.

"Appeal against hydel power project to be taken to deities parliament" The Times of India, 31 August 2011: http://timesofindia.indiatimes.com/city/chandigarh/Appeal-against-hydel-powerproject-tobe-taken-to-deities-parliament/articleshow/9803360.cms.

19 "Villagers protest against power project at Jogini waterfall" by MC Thakur. The Tribune June

12, 2011. http://www.tribuneindia.com/2011/20110612/himachal.htm#6.

"7k women staged a protest against the hydel project on holy waterfall." The Tribune, 26 August 2011.

'Chhor Nullah project cancelled. Villagers jubilant MC Thakur', The Tribune, May 2012.

See the work of[START_REF] Peabody | Inchoate in Kota? Contesting authority through a north Indian pageant-play[END_REF] on Rajasthan.

a Generous support for research leading to this article was provided by the programme "Uomo e natura nel pensiero e nella storia sociale dell'India" funded by the Ministero dell'Istruzione dell'Università e della Ricerca, and also the programme "Presence d'Esprits", funded by the French National Research Agency (ANR). b CNRS, Centre d'Études Himalayennes.


Christophe Bogey
email: christophe.bogey@ec-lyon.fr

Two-dimensional features of correlations in the flow and near pressure fields of Mach number 0.9 jets

In the present study, two-dimensional spatial correlations are calculated in the flow and the near pressure fields of two isothermal round jets at a Mach number of 0.9, computed by highly-resolved simulations using cylindrical coordinates (r , θ, z). The two jets have diameterbased Reynolds numbers of 3, 125 and 100, 000, and they are initially weakly and strongly disturbed, respectively. For both jets, correlations are evaluated between signals at a given point, namely flow fluctuations on the jet axis at the end of the potential core and pressure fluctuations in the jet near field, and 2-D fields acquired in sections (z, r). The full signals but also the axisymmetric and first azimuthal modes are considered. Overall, despite the significant differences in Reynolds number and nozzle-exit conditions, the results for the two jets are very similar. Strong levels of correlations are obtained over large spatial regions and long time periods, providing information on noise generation mechanisms. In particular, the 2-D correlation fields reveal the presence of a wavepacket-like structure growing in the jet mixing layers, centered on a correlation spot in the potential core, and peaking in amplitude around the end of the jet core, which leads to the emission of sound waves in the downstream direction.

I. Introduction

Since more than sixty years [START_REF] Lighthill | On sound generated aerodynamically I. General theory[END_REF][START_REF] Lilley | On the noise from air jets[END_REF], a large amount of studies have been performed to investigate subsonic jet noise. Some questions, however, remain about the low-frequency acoustic component dominating in the downstream direction [START_REF] Mollo-Christensen | Experiments on jet flows and jet noise far-field spectra and directivity patterns[END_REF]. This component, typically centered around a Strouhal number of St D = f D/u j = 0.15, can be measured over a wide range of Mach numbers [START_REF] Tam | Jet noise: Since 1952[END_REF], typically from M = u j /c a = 0.5 up to M = 2, where f is the frequency, D and u j are the jet diameter and velocity, and c a is the speed of sound in the ambient medium. It is mainly axisymmetric [START_REF] Juvé | Filtered azimuthal correlations in the acoustic far field of a subsonic jet[END_REF][START_REF] Cavalieri | Axisymmetric superdirectivity in subsonic jets[END_REF], and has properties which are quite distinct from those of the omnidirectional, broadband noise component prevailing in the upstream and sideline directions, generated by fine-scale turbulence [START_REF] Tam | The sources of jet noise: experimental evidence[END_REF]. Therefore, it seems to be produced by large-scale structures and/or instability waves. Furthermore, it appears to be emitted around the end of the potential core [START_REF] Lee | Phased-array measurements of single flow hot jets[END_REF][START_REF] Panda | Investigation of noise sources in high-speed jets via correlation measurements[END_REF], by a mechanism which is still not clearly understood, but does not depend much on the Reynolds number [START_REF] Kastner | Comparison of noise mechanisms in high and low Reynolds number high-speed jets[END_REF][START_REF] Bogey | An analysis of the correlations between the turbulent flow and the sound pressure field of subsonic jets[END_REF]. Recently, this mechanism has been assumed to be similar to that predicted in theoretical work on noise generation by hydrodynamic wavepackets [START_REF] Tam | The sources of jet noise: experimental evidence[END_REF][START_REF] Suzuki | Review of diagnostic studies on jet-noise sources and generation mechanisms of subsonically-convecting jets[END_REF][START_REF] Jordan | Wave packets and turbulent jet noise[END_REF].

In order to shed light on that mechanism, different methods have been proposed. One method consists in computing cross-correlations between flow quantities and acoustic signals outside the jet. It has been employed since the early seventies in several experimental and numerical investigations [START_REF] Panda | Investigation of noise sources in high-speed jets via correlation measurements[END_REF][START_REF] Bogey | An analysis of the correlations between the turbulent flow and the sound pressure field of subsonic jets[END_REF][START_REF] Lee | Direct correlation of noise and flow of a jet[END_REF][START_REF] Seiner | The distribution of jet source strength intensity by means of direct correlation technique[END_REF][START_REF] Schaffar | Direct measurements of the correlation between axial in-jet velocity fluctuations and far field noise near the axis of a cold jet[END_REF][START_REF] Panda | Experimental investigation of turbulent density fluctuations and noise generation from heated jets[END_REF][START_REF] Bogey | Simulation of a hot coaxial jet: direct noise prediction and flow-acoustics correlations[END_REF][19][START_REF] Henning | Causality correlation analysis on a cold jet by means of simultaneous Particle Image Velocimetry and microphone measurements[END_REF], and very recently for temporallydeveloping jets [START_REF] Bogey | On noise generation in low Reynolds number temporal round jets at a Mach number of 0.9[END_REF]. It has been found that the noise radiated in the downstream direction correlates with the fluctuations near the end of the potential core for high-subsonic and supersonic jets, suggesting a link between the breakdown of shear-layer turbulent structures and the generation of that noise. The spatial structure and characteristics of the sound field have also been investigated from pressure auto-correlations. The downstream noise component is coherent over large spatial areas, as expected for noise from large-scale structures [START_REF] Tam | The sources of jet noise: experimental evidence[END_REF].

In the present work, cross-and auto-correlations are calculated in the flow and the near pressure fields of two isothermal round jets at a Mach number of 0.9 and at Reynolds numbers of 3, 125 and 100, 000. They are computed from data obtained in highly-resolved simulations in 2-D sections (z, r) of the jets, for the full flow and pressure signals and for the azimuthal modes n θ = 0 and 1 alone. Two-dimensional spatial correlations and their time evolutions are thus presented, with the aim of accessing key information on noise generation. Particular attention is paid to the correlations with the fluctuations at the end of the jet potential core, and with the sound pressure fluctuations radiated in the downstream direction, in order to further clarify the mechanism underlying the emission of acoustic waves in that direction.

The paper is organized as follows. The characteristics of the jets and of the simulations, including jet initial conditions, numerical methods and computational parameters, are documented, and the two-dimensional cross-correlations are defined in section II. The main properties of the jet flow and near pressure fields, and the correlations are shown in section III. Finally, concluding remarks are given in section IV.

II. Parameters

A. Jet flow conditions

Two isothermal round jets at a Mach number M = u j /c 0 of 0.9 and Reynolds numbers Re D = u j D/ν of 100, 000 and 3, 125 are simulated, where c 0 , D and ν are the speed of sound in the ambient medium, the jet diameter and the kinematic molecular viscosity, as reported in table 1. The first one has been considered in previous numerical studies [START_REF] Bogey | Large-Eddy Simulation of the flow and acoustic fields of a Reynolds number 10 5 subsonic jet with tripped exit boundary layers[END_REF][START_REF] Bogey | Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based Reynolds number of 10 5[END_REF][START_REF] Bogey | Grid sensitivity of flow field and noise of high-Reynolds-number jets computed by large-eddy simulation[END_REF]. The jets originate from a pipe nozzle of radius r 0 = D/2 and length 2r 0 into a medium at ambient temperature and pressure T 0 = 293 K and p 0 = 10 5 Pa. The pipe exit is at z = 0, and the pipe wall thickness is 0.053r 0 . At the pipe inlet, at z = -2r 0 , Blasius laminar boundary-layer profiles of thickness δ BL = 0.15r 0 for Re D = 100, 000 and δ BL = 0.42r 0 for Re D = 3, 125 are imposed for the axial velocity [START_REF] Bogey | Influence of nozzle-exit boundary-layer conditions on the flow and acoustic fields of initially laminar jets[END_REF]. The boundary layer is thinner at a higher Reynolds number, in agreement with experimental trends [START_REF] Zaman | Effect of initial condition on subsonic jet noise[END_REF][START_REF] Zaman | Effect of initial boundary-layer state on subsonic jet noise[END_REF]. In addition, radial and azimuthal velocities are set to zero, pressure is equal to p 0 , and temperature is determined by a Crocco-Busemann relation. u ′ e /u j 0.9 100, 000 0.15r 0 9% 0.9 3, 125 0.42r 0 1%

The mean and rms axial velocity profiles obtained at the nozzle-exit section for the two jets are presented in figure 1. The mean velocity profiles are very similar to the laminar profiles imposed at the nozzle inlet, while the rms velocity profiles show peak axial turbulence intensities u ′ e /u j of 9.14% for Re D = 100, 000 and of 0.99% for Re D = 3, 125. These turbulence intensities are obtained by adding random low-level vortical disturbances uncorrelated in the azimuthal direction at z = -0.95r 0 in the boundary layers inside the pipe [START_REF] Bogey | Large-Eddy Simulation of the flow and acoustic fields of a Reynolds number 10 5 subsonic jet with tripped exit boundary layers[END_REF]. This forcing procedure allows us to generate disturbed flow conditions at the nozzle exit, which would otherwise be fully laminar. Thus, the present jets are, respectively, initially highly and weakly disturbed. The nozzle-exit conditions for the jet at Re D = 100, 000 correspond to those measured in a tripped jet by Zaman [START_REF] Zaman | Effect of initial condition on subsonic jet noise[END_REF]. They have been discussed in previous papers [START_REF] Bogey | Large-Eddy Simulation of the flow and acoustic fields of a Reynolds number 10 5 subsonic jet with tripped exit boundary layers[END_REF][START_REF] Bogey | On the spectra of nozzle-exit velocity disturbances in initially nominally turbulent jets[END_REF]. Finally, note that despite the difference in Reynolds number and initial conditions, the two present jets are most likely to radiate noise in a similar manner in the downstream direction [START_REF] Kastner | Comparison of noise mechanisms in high and low Reynolds number high-speed jets[END_REF][START_REF] Bogey | An analysis of the correlations between the turbulent flow and the sound pressure field of subsonic jets[END_REF][START_REF] Stromberg | Flow field and acoustic properties of a Mach number 0.9 jet at a low Reynolds number[END_REF][START_REF] Freund | Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9[END_REF][START_REF] Bogey | Investigation of downstream and sideline subsonic jet noise using Large Eddy Simulation[END_REF]. For Re D = 3, 125, however, only large turbulent scales, hence low-frequency sound waves, are expected in the jet flow and acoustic fields which could help us to extract the main features of the noise generation mechanisms associated with the development of coherent structures in a subsonic jet.

B. Numerical methods

The numerical framework is identical to that used in a number of other jet simulations [22-25, 28, 32, 33]. The simulations are carried out using an in-house solver of the three-dimensional compressible Navier-Stokes equations in cylindrical coordinates (r, θ, z) based on low-dissipation and low-dispersion explicit schemes. The axis singularity is taken into account by the method of Mohseni & Colonius [START_REF] Mohseni | Numerical treatment of polar coordinate singularities[END_REF]. In order to alleviate the time-step restriction near the cylindrical origin, the derivatives in the azimuthal direction around the axis are calculated at coarser resolutions than permitted by the grid [START_REF] Bogey | Finite differences for coarse azimuthal discretization and for reduction of effective resolution near origin of cylindrical flow equations[END_REF]. For the points closest to the jet axis, they are evaluated using 16 points, yielding an effective resolution of 2π/16. Fourth-order eleven-point centered finite differences are used for spatial discretization, and a second-order six-stage Runge-Kutta algorithm is implemented for time integration [START_REF] Bogey | A family of low dispersive and low dissipative explicit schemes for flow and noise computations[END_REF]. A sixth-order eleven-point centered filter [START_REF] Bogey | A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations[END_REF] is applied explicitly to the flow variables every time step. Non-centered finite differences and filters are also used near the pipe walls and the grid boundaries [START_REF] Bogey | Influence of nozzle-exit boundary-layer conditions on the flow and acoustic fields of initially laminar jets[END_REF][START_REF] Berland | High-order, low dispersive and low dissipative explicit schemes for multi-scale and boundary problems[END_REF]. At the boundaries, the radiation conditions of Tam & Dong [START_REF] Tam | Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a nonuniform mean flow[END_REF] are applied" with the addition at the outflow of a sponge zone combining grid stretching and Laplacian filtering [START_REF] Bogey | Three-dimensional non reflective boundary conditions for acoustic simulations: far-field formulation and validation test cases[END_REF], to avoid significant acoustic reflections. Small adjustment terms are also added to prevent that mean density and pressure deviate significantly from ambient density and pressure, and no co-flow is imposed.

In the present simulation, the explicit filtering is employed to remove grid-to-grid oscillations, but also, when the mesh grid is not fine enough to compute the smallest turbulent structures, as a subgrid-scale high-order dissipation model in order to relax turbulent energy from scales at wave numbers close to the grid cut-off wave number while leaving larger scales mostly unaffected. The performance of this large-eddy simulation (LES) approach has been assessed in past studies for subsonic jets, Taylor-Green vortices and turbulent channel flows [START_REF] Bogey | Large-Eddy Simulation of the flow and acoustic fields of a Reynolds number 10 5 subsonic jet with tripped exit boundary layers[END_REF][START_REF] Bogey | Large Eddy Simulations of transitional round jets: influence of the Reynolds number on flow development and energy dissipation[END_REF][START_REF] Bogey | Turbulence and energy budget in a self-preserving round jet: direct evaluation using large-eddy simulation[END_REF][START_REF] Fauconnier | On the performance of relaxation filtering for large-eddy simulation[END_REF][START_REF] Kremer | Large-eddy simulation of turbulent channel flow using relaxation filtering: resolution requirement and Reynolds number effects[END_REF], from comparisons with solutions of direct numerical simulations and from the examination of the magnitude and the properties of the filtering dissipation in the wavenumber space.

C. Simulation parameters

The simulation of the jet at Re D = 100, 000 is a well-resolved LES. Its parameters are detailed in a recent paper [START_REF] Bogey | Grid sensitivity of flow field and noise of high-Reynolds-number jets computed by large-eddy simulation[END_REF] reporting the results of a grid-sensitivity study on the jet flow and acoustic fields. The mesh grid contains n r × n θ × n z = 2085 × 1024 × 512 points, and its physical extents are L z = 40r 0 and L r = 15r 0 . The variations of the radial and axial mesh spacings ∆r and ∆z are represented in figure 2. The minimum mesh spacings are equal to ∆r = 0.0036r 0 at r = r 0 and ∆z = 0.0072r 0 at z = 0. The maximal mesh spacing in the jet near field is equal to ∆r = 0.075r 0 , leading to a Strouhal number of St D = f D/u j = 5.9 for an acoustic wave discretized by five points per wavelength, where f is the frequency.

The simulation of the jet at Re D = 3, 125 is a direct numerical simulation. The mesh grid here is made of n r × n θ × n z = 2458 × 512 × 427 points. It extends, excluding the sponge zone, up to L z = 75r 0 in the axial direction and out to L r = 25r 0 in the radial direction. As shown in figure 2, the minimum mesh spacings are equal to ∆r = 0.0072r 0 at r = r 0 and ∆z = 0.014r 0 at z = 0, that are twice as large as those for the jet at Re D = 100, 000. In the jet near field, the maximal mesh spacing is also doubled compared to the higher-Reynolds-number case, with ∆r = 0.15r 0 yielding St D = 3 for an acoustic wave with five points per wavelength.

The simulations have been performed with an OpenMP-based in-house solver, using a time step ∆t of 0.7 × ∆r(r = r 0 )/c 0 for Re D = 100, 000 and of 0.6 × ∆r(r = r 0 )/c 0 for Re D = 3, 125, to ensure numerical stability. The simulation time T after the transient period is equal to 1, 000r 0 /u j for the jet at Re D = 100, 000 and to 2, 000r 0 /u j for the jet at Re D = 3, 125, corresponding to 438, 000 and 511, 000 iterations, respectively. A total number of approximately 2.5 billion CPU hours has thus been consumed, for 200 GB of memory required for the higher-Reynolds-number case. During time T, density, velocity components and pressure along the jet axis at r = 0, and on the surfaces located at r = r 0 and r = L r , are recorded at a sampling frequency allowing spectra to be computed up to St D = 12.8. Density, velocities and pressure obtained at the azimuthal angles θ = 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2 and 7π/4 for Re D = 100, 000 and θ = 0, π/2, π and 3π/2 for Re D = 3, 125 are also stored at a halved frequency. Their Fourier coefficients in the azimuthal directions, estimated over the full section (r, z), are also saved for the first nine azimuthal modes. The statistics are averaged in the azimuthal direction, when possible. The time spectra are evaluated from overlapping samples of duration 45r 0 /u j on the jet axis, and 90r 0 /u j otherwise. In the azimuthal direction, the post-processing is performed up to the mode n θ = 128 for Re D = 100, 000 and n θ = 64 for Re D = 3, 125, where n θ is the dimensionless azimuthal wave number such that n θ = k θ r.

D. Definition of the correlations

In the present work, two-dimensional spatial correlations are computed in the flow and near pressure fields of the two jets. In practice, a signal f 1 at a point r = r 1 , θ = θ 1 and z = z 1 at time t is correlated with a signal f 2 in the 2-D section (r, z) at θ = θ 1 at time t + δt, giving

C(r, z, δt) = f 1 (r 1 , z 1 , t) × g 2 (r, z, t + δt)
where δt is the time delay between the two signals, and . denotes time averaging. Dimensionless correlations R(r, z, δt) = C(r, z, δt)

f 2 1 (r 1 , z 1 , t) 1/2 × f 2 2 (r, z, t) 1/2
are then evaluated. The signals f 1 and f 2 can be the time series of flow and pressure fluctuations issued from the simulations, but also of their Fourier coefficients in the azimuthal direction. The correlations obtained for the different azimuthal angles are averaged, when justified. In this paper, three types of correlations are examined, depending on the signals f 1 and f 2 chosen, as depicted in table 2. In case 1, the fluctuations of axial velocity, vorticity norm and pressure recorded on the jet centerline at z = z c , where z c is defined as the position of the end of the potential core, are correlated with the 2-D fluctuating pressure field. In cases 2 and 3, the pressure fluctuations obtained at r 1 = 15r 0 , at z 1 = 40r 0 and z 1 = z c , respectively, are correlated with the 2-D fields of velocity, vorticity and pressure fluctuations. Therefore, in case 1, the reference 1-D signal is taken in a flow region where the strongest noise sources have been localized experimentally in subsonic jets [START_REF] Lee | Phased-array measurements of single flow hot jets[END_REF][START_REF] Chu | Use of a spherical concave reflector for jet-noise-source distribution diagnosis[END_REF][START_REF] Fisher | Jet engine noise source location: The polar correlation technique[END_REF], and where the disturbances have been found to significantly correlate with the downstream noise [START_REF] Panda | Investigation of noise sources in high-speed jets via correlation measurements[END_REF][START_REF] Bogey | An analysis of the correlations between the turbulent flow and the sound pressure field of subsonic jets[END_REF][START_REF] Schaffar | Direct measurements of the correlation between axial in-jet velocity fluctuations and far field noise near the axis of a cold jet[END_REF]. In cases 2 and 3, the selected 1-D pressure signals are in the jet near field at r = 15r 0 , where acoustic components are stronger than aerodynamic components according to measurements [START_REF] Arndt | The proper orthogonal decomposition of pressure fluctuations surrounding a turbulent jet[END_REF][START_REF] Bogey | Experimental study of the spectral properties of near-field and far-field jet noise[END_REF]. In case 2, in particular, the low-frequency strong acoustic waves radiated by the jets in the downstream direction [START_REF] Tam | The sources of jet noise: experimental evidence[END_REF] are expected to dominate at the point (r 1 , z 1 ) considered [START_REF] Bogey | Experimental study of the spectral properties of near-field and far-field jet noise[END_REF].

f 1 (r 1 , z 1 ) u ′ z , |ω| ′ , p ′ at r 1 = 0 and z 1 = z c p ′ (r 1 = 15r 0 , z 1 = 40r 0 ) p ′ (r 1 = 15r 0 , z 1 = z c ) f 2 (r, z) p ′ u ′ z , |ω| ′ , p ′ u ′ z , |ω| ′ , p ′

III. Results

A. Jet flow and near pressure field 1. Vorticity and pressure snapshots Snapshots of the vorticity norm and pressure fluctuations obtained for the two jets are represented in figure 3. Unsurprisingly, the jet flow develops differently depending on the nozzle-exit conditions and Reynolds number. In the initially highly disturbed jet at Re D = 100, 000, in figure 3(a), the mixing layers contain turbulent structures immediately downstream of the nozzle exit, and very fine scales are visible in the flow. On the contrary, in the initially weakly disturbed jet at Re D = 3, 125, in figure 3(b), the laminar shear layers roll up around z = 10r 0 , which leads to the formation and pairings of coherent vortical structures. Moreover, only large turbulent scales can be seen due to the effects of viscosity at such a low Reynolds number.

In the same way, the pressure field of the jet at Re D = 100, 000 exhibits more high-frequency acoustic waves than the jet at Re D = 3, 125, in particular in the sideline and upstream directions. In both cases, however, large-scale pressure fluctuations, classically attributed to the flow coherent structures [START_REF] Arndt | The proper orthogonal decomposition of pressure fluctuations surrounding a turbulent jet[END_REF][START_REF] Coiffet | Coherent structures in subsonic jets: a quasi-irrotational source mechanism?[END_REF], emerge in the close vicinity of the jets. In addition, strong low-frequency acoustic waves, typical of the downstream jet noise component [START_REF] Mollo-Christensen | Experiments on jet flows and jet noise far-field spectra and directivity patterns[END_REF][START_REF] Tam | The sources of jet noise: experimental evidence[END_REF], propagate in the flow direction for both jets. As in a previous numerical study [START_REF] Bogey | Investigation of downstream and sideline subsonic jet noise using Large Eddy Simulation[END_REF], lowering the jet Reynolds number makes them appear more clearly.

Flow features

The variations of the shear-layer momentum thickness δ θ and of the mean axial velocity u z on the centerline for the two jets are presented in figure 4. Experimental data for isothermal jets at M = 0.9 and Re D ≃ 10 6 are also shown for comparison. In figure 4(a), the mixing layer of the jet at Re D = 100, 000 is found to spread at a nearly constant rate, similarly to the measurements. On the contrary, the mixing layer of the jet at Re D = 3, 125 grows slowly from z = 0 down to z ≃ 10r 0 , but then very rapidly due to the formation and pairings of coherent structures during the laminar-turbulent transition [START_REF] Winant | Vortex pairing : the mechanism of turbulent mixing-layer growth at moderate Reynolds number[END_REF]. These shear-layer developments, caused by two different initial jet flow conditions, are consistent with experimental [START_REF] Browand | Growth of the two-dimensional mixing layer from a turbulent and nonturbulent boundary layer[END_REF][START_REF] Husain | Axisymmetric mixing layer: influence of the initial and boundary conditions[END_REF] and numerical [START_REF] Bogey | Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based Reynolds number of 10 5[END_REF] results.

In figure 4(b), the velocity profile for the high-Reynolds-number jet is good agreement with the measurements at Re D ≃ 10 6 . For both jets, coincidentally given the strong discrepancy in shear-layer growth, the velocity on the jet axis starts to decay around z c = 14.6r 0 , where z c is defined as the axial position at which the centerline mean velocity is equal to 0.95u j . Farther downstream, the velocity decay is faster for the jet at Re D = 3, 125 than for the jet at Re D = 100, 000. This is most likely due to the combined effects of viscosity [START_REF] Bogey | Large Eddy Simulations of transitional round jets: influence of the Reynolds number on flow development and energy dissipation[END_REF] and laminar nozzle-exit conditions [START_REF] Bogey | Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based Reynolds number of 10 5[END_REF] in the former case.

The variations of the rms and skewness values of axial velocity fluctuations u ′

z along the jet centerline between z = 0 and z = 30r 0 are plotted in figure 5. In figure 5(a), the rms velocity profile obtained for the jet at Re D = 100, 000 compare well with the experimental data of Lau et al. [START_REF] Lau | Measurements in subsonic and supersonic free jets using a laser velocimeter[END_REF] for a jet at at Re D = 10 6 . The peak of turbulence intensities, located a few radii downstream of z = z c , is reached slightly farther upstream for the jet at Re D = 3, 125 than for the other. Above all, the peak is stronger in the initially laminar jet because of the laminar-turbulent transition occurring close to the end of the potential core. This result is in line with previous simulations [START_REF] Bogey | Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based Reynolds number of 10 5[END_REF].

Regarding the skewness factor of velocity fluctuations, in figure 5(b), negative values lower than -1.5 are found near z = z c for both jets. As reported in previous studies [START_REF] Bogey | Noise investigation of a high subsonic, moderate Reynolds number jet using a compressible LES[END_REF], including one dealing with temporally developing jets [START_REF] Bogey | On noise generation in low Reynolds number temporal round jets at a Mach number of 0.9[END_REF], they indicate the intermittent occurrence of velocity deficits on the jet centerline when shear-layer vortical structures intrude into the potential core. This flow feature appeared to be one of the reasons for the significant correlations calculated between velocity fluctuations at the end of the jet core and the low-frequency acoustic waves radiated in the downstream direction [START_REF] Bogey | An analysis of the correlations between the turbulent flow and the sound pressure field of subsonic jets[END_REF].

Near-field pressure spectra

The pressure spectra obtained in the jet near field at r = 15r 0 and z = 40r 0 are first represented in figure 6(a) as a function of Strouhal number. The one for the jet at Re D = 100, 000 is in very good agreement with the corresponding measurements [START_REF] Bogey | Experimental study of the spectral properties of near-field and far-field jet noise[END_REF] for an isothermal jet at M = 0.9 and Re D = 7.9 × 10 5 . As expected, given the low angle of radiation relative to the flow direction, of approximately 30 degrees when taking the end of the potential core as origin, the spectra are both dominated by a low-frequency component centered around St D = 0.15 for the jet at Re D = 100, 000 and St D = 0.25 for Re D = 3, 125. The peak levels are however stronger by 5 dB for the jet at Re D = 3, 125, which is consistent with the higher turbulence intensities in that case.

The contributions of azimuthal modes n θ = 0, 1 and 2 to the pressure spectra at r = 15r 0 and z = 40r 0 are shown in figure 6(b) for Re D = 100, 000 and in figure 6(c) for Re D = 3, 125. For the two jets, for St D ≤ 0.3, the contribution of the axisymmetric mode is greater than that of mode n θ = 1 by between 3 and 6 dB, which is itself approximately 6 dB above that of mode n θ = 2. A similar prevalence of the axisymmetric mode is found in the far pressure field of jets in the downstream direction [START_REF] Juvé | Filtered azimuthal correlations in the acoustic far field of a subsonic jet[END_REF][START_REF] Cavalieri | Axisymmetric superdirectivity in subsonic jets[END_REF]. The pressure spectra obtained at r = 15r 0 and z = z c , perpendicularly to the end of the potential core, are then depicted in figure 7(a). Compared to those of figure 6(a), they exhibit levels lower by typically 8 dB, and they are broader. The latter remark is particularly true for the jet at Re D = 100, 000, whose spectrum has a shape closely following that of the spectrum acquired experimentally [START_REF] Bogey | Experimental study of the spectral properties of near-field and far-field jet noise[END_REF] at r = 15r 0 and z = 14r 0 for a Mach 0.9 jet at a high Reynolds number over the whole frequency range up to St D = 4.8. On the contrary, the spectrum for the jet at Re D = 3, 125 contains negligible high-frequency components for St D > 1.2, due to the disappearance of fine-scale turbulence at such a low Reynolds number.

Finally, as previously, the contributions of modes n θ = 0, 1 and 2 to the pressure spectra are displayed in figure 7(b) for Re D = 100, 000 and in figure 7(c) for Re D = 3, 125. In both cases, no mode emerges clearly, and modes n θ = 0, 1 and 2 are predominant, respectively, for St D 0.25, for 0.25 St D 1.2 and for higher frequencies. A distribution of the acoustic energy between the first three azimuthal modes has also been measured in far field in the sideline direction [START_REF] Juvé | Filtered azimuthal correlations in the acoustic far field of a subsonic jet[END_REF].

B. Two-dimensional correlations

Correlations with fluctuations at the end of the potential core (case 1 in section II.D)

The normalized correlations R evaluated between the fluctuations of axial velocity, vorticity and pressure on the jet axis at z = z c and the 2-D fluctuating pressure field for the axisymmetric mode for the jet at Re D = 100, 000 are represented in figure 8, from top to bottom. The results obtained for the three time delays of δt = -8r 0 /c 0 , 0 and 16r 0 /c 0 are shown, from left to right. Significant levels of correlations, higher than 0.2, are found both in the jet and the near pressure fields. For δt = -8r 0 /c 0 , a wavy structure appears in the flow and its in immediate vicinity, especially in figures 8(a,g). The axial position of this structure, illustrated by a vertical line, indicates a convection at a velocity of approximately 0.7u j . The correlation levels increase with time and reach a peak for δt = 0, as expected. At later times, the structure vanishes rapidly, but elongated spots of correlation propagate downstream in the pressure field, see right figures for δt = 16r 0 /c 0 . These spots are roughly aligned with a circle of radius c 0 δt centered on r = 0 and z = z c . They display negative values for the axial velocity in figure 8(c) and positive values for the vorticity in figure 8(i), which is in accordance with previous studies [START_REF] Bogey | An analysis of the correlations between the turbulent flow and the sound pressure field of subsonic jets[END_REF][START_REF] Bogey | On noise generation in low Reynolds number temporal round jets at a Mach number of 0.9[END_REF]. The present results reveal the connection between the growth and decay of a large-scale, oscillatory structure in the jet flow and the radiation of a strong acoustic wave in the downstream direction. This mechanism is similar to that predicted in theoretical work on noise generation by hydrodynamic wavepackets in high-speed jets [START_REF] Tam | The sources of jet noise: experimental evidence[END_REF][START_REF] Suzuki | Review of diagnostic studies on jet-noise sources and generation mechanisms of subsonically-convecting jets[END_REF][START_REF] Jordan | Wave packets and turbulent jet noise[END_REF], but also to that recently identified for temporal jets using conditional averaging [START_REF] Bogey | On noise generation in low Reynolds number temporal round jets at a Mach number of 0.9[END_REF]. As in figure 8, the correlations R determined between axial velocity, vorticity and pressure at the end of the potential core and the 2-D pressure field for mode n θ = 0 for the jet at Re D = 3, 125 are provided for δt = -8r 0 /c 0 , 0 and 16r 0 /c 0 in figure 9. Compared to the jet at Re D = 100, 000, they exhibit higher levels, but bear obvious similarities. In particular, the wavepacket-like structure developing and convected at ∼ 0.7u j in the flow is clearly visible for negative time delays. This is also the case for the spots of correlation propagating at a speed of c 0 in the pressure field for positive time delays. These results further relate the generation the axisymmetric noise component dominant in the downstream direction of jets [START_REF] Juvé | Filtered azimuthal correlations in the acoustic far field of a subsonic jet[END_REF][START_REF] Cavalieri | Axisymmetric superdirectivity in subsonic jets[END_REF] to a mechanism occurring in the jet core region over a long time and a large spatial extent. They also supports the weak dependence of that mechanism on the Reynolds number [START_REF] Kastner | Comparison of noise mechanisms in high and low Reynolds number high-speed jets[END_REF][START_REF] Stromberg | Flow field and acoustic properties of a Mach number 0.9 jet at a low Reynolds number[END_REF][START_REF] Bogey | Investigation of downstream and sideline subsonic jet noise using Large Eddy Simulation[END_REF].

Correlations with downstream near-field pressure (case 2 in section II.D)

The normalized correlations R obtained between p ′ at r = 15r 0 and z = 40r 0 and p ′ in the 2-D section (z, r) from the full signal the modes n θ = 0 and of pressure are represented in figure 10 for the time delay of δt = -12r 0 /c 0 , from left to right. The results for the jets at Re D = 100, 000 and 3, 125 are provided in the top and bottom figures, respectively. The correlation levels are greater for Re D = 3, 125 than for Re D = 100, 000, as expected given the pressure snapshots of figure 3, but also for the axisymmetric mode than for the mode n θ = 1. In all cases, however, a front of correlations close to 1, whose origin seems to be roughly at the end of the jet potential core, and whose minimal distance from the point at r = 15r 0 and z = 40r 0 is equal to c 0 δt, is observed. This front extends over a very wide range of polar angles, and is surrounded by two fronts of negative correlations. These correlation fields show the high coherence of the jet acoustic components in the downstream direction [START_REF] Tam | The sources of jet noise: experimental evidence[END_REF] at both low and high Reynolds numbers [START_REF] Kastner | Comparison of noise mechanisms in high and low Reynolds number high-speed jets[END_REF][START_REF] Bogey | An analysis of the correlations between the turbulent flow and the sound pressure field of subsonic jets[END_REF].

In order to explore the generation of these noise components, the non-normalized correlations C obtained between p ′ at r = 15r 0 and z = 40r 0 and the fluctuations of axial velocity in the flow and of pressure outside for the jet at Re D = 3, 125 are represented in figure 11 for δt = -36r 0 /c 0 , -28r 0 /c 0 and -15r 0 /c 0 , from left to right. For the axisymmetric mode, in the top figures, a wavepacket-like structure grows in the very near pressure field of the jet. Its amplitude is maximum around δt = -28r 0 /c 0 , when it passes through the end of the potential core, and then weaker. Simultaneously, an acoustic wave is radiated in the jet direction, and gradually deviates from the flow. This process is similar to that revealed in figure 8 for the case 1 of correlations. In the present figure, the wavepacket-like structure is moreover connected to a spot of negative correlations between the downstream near-field pressure and the velocity fluctuations in the flow. This spot develops on the high-velocity side of the mixing layer, and is strongest on the jet axis around the time of sound emission. Such a spot was previously found when the potential core of temporally developing jet closes [START_REF] Bogey | On noise generation in low Reynolds number temporal round jets at a Mach number of 0.9[END_REF]. It has been attributed to the presence of a velocity deficit when vorticity enters into the jet core.

For the mode n θ = 1, in the bottom of figure 11, a wavy structure is convected in the near pressure field surrounding the jet, strengthens down the end of the jet core, and subsequently weakens and radiates sound pressure waves, as for the mode n θ = 0. This structure is also attached to a spot of negative pressure-velocity correlations in the flow, which are nil on the jet axis in this case. These results suggest that the generation process of the acoustic mode n θ = 1 is of the same nature of that of the axisymmetric component in the jet downstream direction.

Correlations with sideline near-field pressure (case 3 in section II.D)

The normalized correlations R estimated between p ′ at r = 15r 0 and z = z c and p ′ in section (z, r) from the full signal and the modes n θ = 0 and 1 of pressure are represented in figure 12 for the time delay of δt = -3r 0 /c 0 , from left to right. As in figure 10, the results obtained for the jets at Re D = 100, 000 and 3, 125 are given in the top and bottom figures, respectively. Significant levels of correlation are found, especially for the axisymmetric mode. They are higher, and extend over a wider region for the lower Reynolds number jet, compare for instance figures 12(a) and 12(d), indicating that the noise radiated in the sideline direction is more coherent in this case. This results from the fact the sound waves propagating in this direction are generated by large-scale structures developing in the mixing layers for the initially laminar jet at Re D = 3, 125, whereas they are produced by a broad range of turbulent scales distributed over a large axial distance for the initially highly disturbed jet at Re D = 100, 000, as suggested by the pressure snapshots of figure 3. Finally, the non-normalized correlations C calculated between p ′ at = 15r 0 and z = z c and the fluctuations of axial velocity in the flow and of pressure outside for the jet at Re D = 100, 000 are shown in figure 13 for δt = -15r 0 /c 0 , -12r 0 /c 0 and -6r 0 /c 0 , from left to right. For the axisymmetric mode, on top, the results are roughly similar to those obtained for the correlations with the pressure fluctuations at r = 15r 0 and z = 40r 0 . Indeed, a wavepacket-like structure, connected to a spot of negative correlations with velocity fluctuations in the flow, is found to be convected and to generate sound pressure waves propagating preferentially in the downstream direction. More surprisingly, positive values of correlation are noted in the jet flow downstream of this spot almost down to z = 40r 0 . For the mode n θ = 1, on bottom, a wavepacket-like noise generation mechanism also appears in the correlation fields, albeit less markedly than above. In figure 13(e), in addition, the correlations are strong over a significant part of the circle of radius c 0 δt centered on the observer point at r = 15r 0 and z = z c , suggesting that they results from several sources in the jet.

IV. Conclusion

In this paper, cross-and auto-correlations calculated in the flow and the near pressure fields of subsonic round jets in sections (z, r) are presented for two jets at a Mach number of 0.9 and at Reynolds numbers of 3, 125 and 100, 000, with weakly and highly disturbed nozzle-exit boundary layers, respectively. Their two-dimensional structures and time evolutions provide information on the noise radiated by high-subsonic jets and its generation in the jet flows. Concerning the noise emitted in the downstream direction, in particular, strong correlation levels are obtained over very large spatial areas and long time periods. This is true for the pressure auto-correlations in the acoustic field showing the coherence of the sound waves propagating in the jet direction, but also for the cross-correlations computed from aerodynamic disturbances inside and immediately around the flow. In the latter case, a wavepacket-like structure emerges early on in the mixing layers, grows in amplitude as it is convected down to the end of the jet potential core, and then weakens gradually. This structure is connected to a spot of negative correlations between sound pressure and velocity in the flow, but also and especially to the acoustic waves generated in the downstream direction. It can be noted that similar results are found for the full flow and sound fields but also for the modes n θ = 0 and 1 taken alone, for both jets. Therefore, the corresponding generation mechanisms appear to be relatively insensitive to the jet Reynolds number and to the initial state and development of the mixing layers. Their characteristics will be explored by further analyses of the present correlation fields.

Fig. 1

 1 Fig. 1 Nozzle-exit radial profiles of (a) the mean axial velocity u z and (b) the rms values of axial velocity fluctuations u ′ z for the jets at Re D = 100, 000 and Re D = 3, 125.

Fig. 2

 2 Fig. 2 Variations of (a) the radial mesh spacing ∆r/r 0 and (b) the axial mesh spacing ∆z/r 0 for the jets at Re D = 100, 000 and Re D = 3, 125.

Fig. 3

 3 Fig. 3 Representation of vorticity norm inside the flow and of pressure fluctuations outside, for the jets at (a) Re D = 100, 000 and (b) Re D = 3, 125. The color scales range between ±6u j /r 0 and ±70 Pa, from blue to red.

Fig. 4

 4 Fig. 4 Variations of (a) the shear-layer momentum thickness δ θ and (b) the mean axial velocity u z on the centerline for the jets at Re D = 100, 000 and Re D = 3, 125; measurements for isothermal jets at M = 0.9 at •, Re D = 10 6 [53, 54] and ⋄ Re D = 7.7 × 10 5 [55].

Fig. 5

 5 Fig. 5 Variations of (a) the rms values and (b) the skewness factors of the axial velocity fluctuations u ′ z on the centerline for the jets at Re D = 100, 000 and Re D = 3, 125; measurements for isothermal jets at M = 0.9 at • Re D = 10 6 [53] and ⋄ Re D = 7.7 × 10 5 [55].

Fig. 6

 6 Fig. 6 Sound pressure levels (SPL) obtained at r = 15r 0 and z = 40r 0 as a function of St D : (a) SPL for the jets at Re D = 100, 000 and Re D = 3, 125; (b, c) SPL and contributions of modes n θ = 0, n θ = 1 and n θ = 2 for (b) Re D = 100, 000 and (c) Re D = 3, 125; ▽ measurements for an isothermal jet at M = 0.9 and Re D = 7.9 × 10 5 [48].

Fig. 7

 7 Fig. 7 Sound pressure levels (SPL) obtained at r = 15r 0 and z = z c as a function of St D : (a) SPL for the jets at Re D = 100, 000 and Re D = 3, 125; (b, c) SPL and contributions of modes n θ = 0, n θ = 1 and n θ = 2 for (b) Re D = 100, 000 and (c) Re D = 3, 125; ▽ measurements at r = 15r 0 and z = 14r 0 for an isothermal jet at M = 0.9 and Re D = 7.9 × 10 5 [48].

Fig. 8

 8 Fig. 8 Jet at Re D = 100, 000. Correlations R of (top) u ′ z , (middle) |ω| ′ and (bottom) p ′ at r = 0 and z = z c with p ′ (r , z) for (left) δt = -8r 0 /c 0 , (center) δt = 0 and (right) δt = 16r 0 /c 0 , for n θ = 0; positions for a downstream convection at 0.7u j and a sound propagation at c 0 . The color scale ranges between ±0.25, from blue to red.

Fig. 9

 9 Fig. 9 Jet at Re D = 3, 125. Correlations R of (top) u ′ z , (middle) |ω| ′ and (bottom) p ′ at r = 0 and z = z c with p ′ (r , z) for (left) δt = -8r 0 /c 0 , (center) δt = 0 and (right) δt = 16r 0 /c 0 , for n θ = 0; positions for a downstream convection at 0.7u j and a sound propagation at c 0 . The color scale ranges between ±0.25, from blue to red.

Fig. 10 Correlations

 10 Fig. 10 Correlations R between p ′ (r = 15r 0 , z = 40r 0 ) and p ′ (r , z) for δt = -12r 0 /c 0 , at (top) Re D = 100, 000 and (bottom) Re D = 3, 125: (left) full field, modes (center) n θ = 0 and (right) n θ = 1;positions for a at c 0 . The color scale ranges between ±1, from blue to red.

Fig. 11

 11 Fig. 11 Jet at Re D = 3, 125. Correlations C of p ′ (r = 15r 0 , z = 40r 0 ) with u ′ z (r ≤ 1.75r 0 , z) and p ′ (r > 1.75r 0 , z) for (left) δt = -36r 0 /c 0 , (center) δt = -28r 0 /c 0 and (right) δt = -15r 0 /c 0 , for modes (top) n θ = 0 and (bottom) n θ = 1: positions for a sound propagation at c 0 . The color scales range between ±0.02u j × p ′ r ms

Fig. 12

 12 Fig. 12 Correlations R between p ′ (r = 15r 0 , z = z c ) and p ′ (r , z) for t -3r 0 /c 0 at (top) Re D = 100, 000 and (bottom) Re D = 3, 125: (left) full field, modes (center) n θ = 0 and (right) n θ = 1; positions for a sound propagation at c 0 . The color scale ranges between ±1, from blue to red.

Fig. 13

 13 Fig. 13 Jet at Re D = 100, 000. Correlations C of p ′ (r = 15r 0 , z = z c ) with u ′ z (r ≤ 1.75r 0 , z) and p ′ (r > 1.75r 0 , z) for (left) δt = -15r 0 /c 0 , (center) δt = -12r 0 /c 0 and (right) δt = -6r 0 /c 0 , for modes (top) n θ = 0 and (bottom) n θ = 1; positions for a sound propagation at c 0 . The color scales range between ±0.02u j × p ′ r ms

Table 1 Jet parameters: Mach and Reynolds numbers M and Re D , thickness of the Blasius laminar boundary- layer profile imposed at the pipe nozzle inlet δ BL , peak turbulence intensity at the nozzle exit

 1

	M	Re D	δ BL

u ′ e /u j .

Table 2 Types of two-dimensional spatial correlations.

 2

	signals	case 1	case 2	case 3

Downloaded by Christophe Bogey on January 7, 2019 | http://arc.aiaa.org | DOI: 10.2514/6.2019-0806

Downloaded by Christophe Bogey on January 7, 2019 | http://arc.aiaa.org | DOI: 10.2514/6.2019-0806

Acknowledgments

This work was granted access to the HPC resources of FLMSN (Fédération Lyonnaise de Modélisation et Sciences Numériques), partner of EQUIPEX EQUIP@MESO, and of the resources of CINES (Centre Informatique National de l'Enseignement Supérieur) and IDRIS (Institut du Développement et des Ressources en Informatique Scientifique) under the allocation 2018-2a0204 made by GENCI (Grand Equipement National de Calcul Intensif). It was performed within the framework of the Labex CeLyA of Université de Lyon, operated by the French National Research Agency (Grant No. ANR-10-LABX-0060/ANR-11-IDEX-0007).