Benjamin Dorman Co

Nicolas Lainé

Keywords: ritual, territorial cult, appropriation of local deities, Khamti, Arunachal Pradesh

France), and serves as an expert member of the IUCN SSC Asian Elephant Specialist Group.

Phi Muangs, Forces of the Place among the

Phi Muangs, Forces of the Place for the Khamti in Arunachal Pradesh (Northeast India)

This article focuses on the cult dedicated to the phi muang, a type of primordial divinity for the Khamti 1 , a Shan population that inhabits the Arunachal Pradesh in India 2 . Like other Tai societies across Southeast Asia, the Khamti live in the lowlands and practice irrigated paddy field cultivation. In India, an important aspect of their livelihood is their attachment to elephants, which are still mainly used for the timber industry. This activity was the force behind the Khamti economic development since Indian Independency in 1947 till the end of the last century 3 .

The Khamti migrated to Northeast India from present-day Myanmar in successive waves, beginning from the middle of the 18th century [START_REF] Gogoi | The Tai and the Tai Kingdoms. With a Fuller Treatment of the Tai-Ahom Kingdom in the Brahmaputra Valley[END_REF][START_REF] Terwiel | Tai of Assam: Sacrifices and time reckoning[END_REF]. At that time, their settlement was facilitated by the presence of another Shan population, the Ahom, who had settled there since the 13th century and dominated the region. The vernacular sources available on the region, notably the Buranji (historical chronicles), mention that in 1751, the Ahom king in power at that time authorized the Khamti to settle along the Tengapani river, which is located in the present Lohit district, a place that they used for the growth of irrigated crops. Unlike the Ahom, who had adopted the Hindu religion by the time of the Khamti's arrival [START_REF] Devi | Ahom-Tribal Relations. a Political study[END_REF]), the Khamti are followers of Theravada Buddhism. Since colonial times, the Buddhist doctrine has been presented as the sole religion of the Khamti 4 ; this is reinforced today by a reaffirmation of Shan identity based on Buddhism (Nathalang 2009). However, like other Tai Buddhist populations 5 in Southeast Asia, the religious system of the Khamti is much more complex. It includes elements related to the cult of spirits (phi), as well as others that are a result of interactions with other populations from the Northeast, as well as with other Tai populations across the peninsula. Similar to research done by anthropologist Nicola Tannenbaum on the Shan in North-Western Thailand or by other researchers in South Asia, all these practices and beliefs, rather than being opposed and/or dichotomous 6 , are viewed by scholars to constitute a coherent system.

Among the various components that comprise the religious system of the Khamti, the cult dedicated to the phi muang is viewed as the most important one. The deity associated with it, the phi muang, must be appeased before any individual or collective enterprise is embarked upon. According to the Khamti, there are three phi muang that represent three distinct territories in the Northeast Indian zone. These deities are individualized and personified by different names: Chao Noi Cheynam, Chao Noi Tipam and Nang Hoo Toung. The first two appear to be male spirits, as the title Chao, meaning 'chief', indicates; while the third one refers to a female deity, since any women in this society are addressed through the use of the prefix nang. To obtain protection from the phi muang and/or to ensure success and prosperity, the phi muang must be fed with a sacrifice that is offered to each of them over the course of the same ritual.

The nature of the offering differs, according to the invoked spirit. For example, for Chao Noi Cheynam, a pair of red chickens, a kai may niang (red rooster) and a kai fu niang (red hen) must be offered; for Chao Noi Tipam, the pair must be white; and finally, to feed Nang Hoo Tung, one must offer either a goat (pia) or a pair of ducks (peit, Ass.), with one being a male and the other a female. Such offerings should be performed by a specialist, who will act as an intermediary between the community and the divinity. It is through this sacrifice that this specialist will enter into communication with the divinity concerned, to ask for protection and prosperity from him or her.

I will begin by contextualizing the ritual expressions associated with the phi muang, which will be based on the description of two associated territorial cults 7 : the ceremony carried out in the context of wild elephant capture operations, and the one carried out on a village level for all its inhabitants on the agricultural New Year. These descriptions will thus serve to highlight the essential characteristics of phi muangs among the Khamti. Drawing from records on history from the region, I will then return to the historical and mythological origin of each phi muang, as well as look at the relations that the Khamti maintain with them and how their respective territory are locally thought. By uncovering the spatial configuration of these local forces, I will formulate several hypotheses regarding the integration of the Khamti in a region located at the margins of India.

Ritual expressions associated with phi muangs

Phi muang in elephant capture operations

Since settling in northeast India, the Khamti have captured, trained and worked with elephants 8 . While the work performed with and by elephants has constantly evolved over different time periods, the animal still serves as one of the main sources of income for many Khamti households. In addition, elephants have always been used for domestic purposes (such as a means of transportation for many activities, including hunting, fishing, agricultural work, and firewood collection). Today, elephants are mainly used for logging work. Furthermore, some Khamti are still seasonally engaged in elephant capture operations 9 , despite this activity now being illegal.

Each of these capture operations requires a set of ritual practices based on different beliefs to be carried out before, during, and after the expeditions 10 . These combine rituals associated with Tai populations of Southeast Asia, such as the use of divination charts, and the belief in Utingna 11 (a forest divinity in charge of wild elephants). In addition, other rituals or beliefs have been borrowed from other Northeast Indian populations, such as the Moran and Singpho. Spirit cults devoted to phi muang are also added to these components, along with domestic spirits and phi hai and references to Theravada Buddhism. Buddhism remains quite present, although unofficially since the practise of capturing or killing animal contradicts the doctrine. However, the reference to Buddhism is evident in the consideration of sacred days, the satang, in which it is forbidden for anyone to go into the forest. Among the numerous rituals practices and beliefs enumerated above 12 , the sacrifice offered to one of the three phi muang would be the most important. No catching expedition can be carried out without first nourishing the phi muang. This ritual is mandatory and was mentioned by all the capturers that were interviewed. Among the team members of each expedition, the main phandi 13 (i.e. the elephant's catcher) had the responsibility of offering the sacrificed animal and feeding the phi muang on behalf of all the team members, including the domestic elephants who take part in it.

Interestingly, during capture operations, the sacrifice would not be addressed to the phi muang at the phandi's residence, but to the one in the territory where the operation was taking place. For example, if it has been decided to capture an animal in Chao Noi Tipam's territory, while the phandi resides in Chao Noi Cheynam's territory, the capturer must feed the former prior to entering into its territory. Only upon returning from the expedition will he perform another ritual which would be dedicated to Chao Noi Cheynam. This would be to ask him to host the animal and to protect him. This second ceremony must be performed before the setting up of the camp required for the operation that will then be used to help socialize the elephant.

However, in the case where the territory chosen for the capture is the same as the residence of the capturer, a single ceremony would suffice. The ritual is then performed prior to entering the forest, and could be made at the village altar dedicated to the phi muang, named pang suea muang 14 (see supra.). In this case, the feeding ceremony is made both to seek protection from the phi muang, as well as to inform him of their intention to capture an elephant.

The ritual sacrifice is generally made on the day of departure. Indeed, an elephant catcher that I met in the village of Chongkham informed me that he performed the sacrifice a few days prior to departure. He also added that the ceremony took place at night, directed at the altar of his own village. He said this was possible only because he was going to capture an elephant within his village's territory.

In all other cases, the practice of feeding the phi muang is always held when first entering in the forest. It should be noted that at the entrance of each forest, there would be a specific altar for receiving the offering that is required for each forest activity. However, possibly due to the illegal nature of capture operations today, the catcher that was interviewed told me that they made their own small discreet altar in the forest prior to setting up a temporary camp. This way, they can avoid being exposed or indicating to others the reason for their presence in the forest. At the same time, they can ward off the evil eye for the period of time that they spend in forest 15 . Finally, capturers feed their own phi muang in a personal capacity, particularly if the territorial spirit is different from the one where the capture takes place. This way, they are able to seek additional protection in the same way as they do with the domestic deity who protects their home, the phi hun.

The annual collective ceremony at the village level

In each Khamti's village, a small altar that is devoted to phi muang can be found. The altar is located outside the general village habitation area, and can be found either next to a large tree or at the edge of a river. This place is called the pang suea muang, which literally translates to the 'place for the territorial divinity'. Apart from domestic altar spirits that are present in each household compound, the pang suea muang remains the only material expression of the existence of the phi spirit cult within the Khamti villages.

Each phi muang is not specific to any particular village, but is considered to be the protector of an entire territory that could include several villages, as well as forest areas (pa). It should be mentioned that in contrast to various other Tai populations across Southeast Asia 16 , there are no any specific spirit deities associated to a particular village, which are usually called phi ban (literally, "the spirit of the village"). Indeed, throughout the numerous villages and locations visited during the course of the fieldwork, no Khamti could mention the existence of a village spirit. In addition, it can be noted that phi muang does not necessarily refer solely to a divinity in connection with the human ancestors of the inhabitants of a village, as it is sometimes the case for the phi ban, as this deity does not exist among the Khamti. However, the territorial phi muang is collectively appeased by a sacrificial rite within the village annually. These ceremonies occurred in every village and it is compulsory for every one of its habitants to contribute, attend, and participate in it. Such ceremonies would be the only collective one devoted to the phi muang. Even though each phi muang is associated with several villages, there are no other collective ceremonies that are above the village level. The collective sacrifice offered to the phi muang must be performed at the beginning of each agricultural year, after the Shangken Festival, which would therefore mark the New Year and the beginning of the agricultural calendar, which occurs usually in the second half of April. Without this ceremony, which involves the participation of the entire village with the exception of monks and pregnant women, no field work can begin. At the village level, this collective ceremony requires the presence of a specialist officiant, the phou muang. This specialist oversees the addressing of the sacrifice on behalf of the entire community. Interestingly, I also learned that many phandi are or were the representative phou for their village. Through this act, the specialist will enter into communication with the concerned deity to ask for protection and prosperity, voicing their hope for a good harvest, protection against wild animals, and defence against diseases 17 .

The officiant is the one who will oversee any interaction with the divinity, before asking the village chief (gaon burha, assamese term) to deposit the offering as a sign of allegiance of the entire community. The phou muang is facilitated by an assistant, who oversees the preparation of food that is first served to the divinity and then shared by the villagers. This assistant must be a young, single, and healthy man. In 2010, in the village of Jenglai, the assistant was the son of the phou muang. A few days before the ceremony, the village head gaon burha (assamese) brought together the men to decide on a suitable Sunday to hold the ceremony. Following this meeting, two youth were assigned to collect the donations that would be used to purchase the ritual necessities (incense, candles), including the sacrificial animal. Indeed, it is compulsory for each household to contribute money for the purchases. In addition, each household has to offer a bag of rice, which was mixed as a whole, which will then be cooked and served to village members. A ladle of grain was taken in each bag; this was cooked separately, and presented to the phi muang.

On the morning of the ceremony, most of the men from the village gathered at the altar and, under the orders of the village chief, cleaned the area around it. This involved clearing the brush and making the enclosure ready to welcome the divinity. A bamboo fence was also rebuilt for the occasion. We were in the pre-monsoon period, and it was agreed that the preparation of the offerings (a pair of chickens, black and red, in reference to Chao Noi Cheynam), would take place in a more sheltered place. It was decided that the location would be within the village school, which was located a few hundred meters from the altar. The officiant's son was in charge of the food. Consequently, he killed the animals, skinned them, and then began to prepare the food. During this time, he also mixed all the bags of rice harvested from the villagers and started to cook it.

The men who remained near the altar of the divinity completed the cleaning and decorating of the altar. Small coloured banners were added around the shelter, and the floor under the altar was covered with candles (due to the rain). On the altar, incense and banana leaves were added to receive the food.

Once the dish was prepared, there was a need to gather all the villagers around the altar, before the village chief asked to proceed. There, the villagers sat or squatted outside the enclosure, facing the altar. With the men and young boys were in front, and the women behind, the officiant began to recite a prayer, with his assistant standing aside with the two dishes in his hands in preparation to serve it to the deity. The request was brief and then the divinity was served. Through the voice of the officiant and the offerings, which will be deposited by the village chief, the whole community comes together to ask the Chao Noi Cheynam for protection and prosperity. Once the dishes were served to the deity, the villagers began to pray together, before the chief closes the fence to let the divinity consume the offering. As the rain started to get violent, everyone congregated at school to share in the collective meal.

Photo 1-Altar devoted to Noi Cheynam during the annual ceremony (author, 2010)

Phi muangs: protectors of villages, forests and their inhabitants

With the help of these two short ethnographic descriptions, let us see how we can characterise the phi muang and their various roles and functions among the Khamti.

Firstly, the notion of muang is itself essential for the Khamti, and more generally for Tai people. If we look at [START_REF] Cushing | A Shan and English dictionary[END_REF] dictionary of the Shan language, the notion of muang would refer to a country and/or a kingdom, which would mean to be an area larger than the village itself. A semantic study by Ranee [START_REF] Lertleumsai | Muang as a socio-political unit in Shan concept[END_REF] revealed that, among Shan populations, "muang" generally refers to a geo-socio-political entity (2007). Indeed, the presentation of two territorial cults that are associated with phi muang revealed that among the Khamti, each one had the particularity of exercising its power over several villages, along with integrating certain parts of the adjacent forest area.

Across Southeast Asia, the Tai are organized and structured around the notion of muang (which can also be called mong, ming, maeng, moeng, according to the specific Tai language [START_REF] Michel | L'Asie d'entre Inde et Chine[END_REF]). This notion has been the subject of several anthropological inquiries. According to [START_REF] Taillard | [END_REF], muang was: "Inseparable from the tai identity, the political structure of the müang, both segmental and topocentric (organised from a centre), thus appears as a historically stable element which still constitutes the basis of the local territorial organisation" [START_REF] Taillard | [END_REF]. [START_REF] Tambiah | Buddhism and the spirit Cults in North-East Thailand[END_REF] referred to galactic systems while Condominas (1968) drew from the image of the parasol. In the interpretation offered by [START_REF] Evrard | Chroniques des Cendres. Anthropologie des sociétés khmou et des dynamiques interethniques du Nord-Laos[END_REF], while the term can refer to the level of political hierarchy immediately above that of the village; this can be difficult to translate since it designates both the political power and the territory in which it is exercised over.

Secondly, it should be noted that the collective ceremony related above is found in other Tai populations in Southeast Asia, with different variations. This includes the role of the officiant, the exclusive character of the offering with the exception of the monks, and the role of the village chief. Such ritual ceremonies (regardless of whether animal sacrifices are included) have been described by [START_REF] Durrenberger | Annual non-bhuddist religious observance in Maehongson Shan[END_REF] in Thailand, Condominas (1968), and more recently, Bouté (2012) in Laos. All of these researchers describe a ritual ceremony that is held at the village level for the village spirit. Nevertheless, as said before, no Khamti interviewed who could recall the existence of a village deity specific to a single village.

Contrary to other Tai populations, in the present case there was no protective spirit specifically associated with a single village.

So far, we have seen that the phi muang can both be celebrated individually and collectively link with agricultural and forestry activities. In addition, throughout the year, people freely go to address the phi muang for personal purposes. For example, if there is a theft of cattle in the village, one can come to the phi muang to seek justice. These particular operations are usually carried out at night, without anyone's knowledge. Thus, it appears that among the Khamti, phi muan can refer to a function of regulating social relations within the village. This would thus serve the role of a village spirit which, as already mentioned, does not exist among the Khamti. In this particular case study, the hierarchy of the various spirit cults from household to village to a larger territory, as highlighted by Tanabe (1988) for the Tai Lue, seems to skip an important level: that of the village. Instead, the village level protection only relies on Buddhism and the phi muang. Yet, it should be noted that the latter does not just protect the village and its inhabitants.

Another aspect of the phi muang among the Khamti relies on the nature of the power exercised by the associated divinity. The phi muang appears to be the guardian spirits of an entire territory, including all its components-forest, rivers and mountains, as well as all the living beings, including both humans and non-humans. Khamti villagers also come to address the phi muang whenever they start forest activities. The deity would then function as the divine mediator between men and the territory's natural resources. Here, phi muang serves the main functions of being both protector and bringer of prosperity to the Khamti. The phi muang's intermediary role is the reason as to why we have seen Khamti elephant hunters lend a double allegiance, first to the phi muang corresponding to the place of capture, then to the one corresponding to their residence where the captured animal is destined to live. Such aspects thus highlight the essential role of the phi muang in the control of any living beings present in its territory. Moreover, within elephant capture operations, the various phi muangs compose a spatial organization and stress the importance of integrating the village with parts of the forest.

Following [START_REF] Mus | Cultes indiens et indigènes au Champa[END_REF], a collective work edited by [START_REF] Schlemmer | Rituals, Territories and Powers in the Sino-Indian Margins[END_REF] recently stated the notion of the 'force of the place' as the starting point for an analysis that studies the different territorial cults and ritual expressions in the Sino-Indian margins. Case studies helped highlight the diversity of these supernatural forces, and made direct references to and are "tied to soil, water, forest and game, these entities are the masters of nature's resources." (Schlemmer 2012, 9). Furthermore, one of the main characteristics of the 'forces of the place' would be in the explicit reference to it within a defined territory, in which they exercise control over an entire set of beings, irrespective to their local and spatial properties (from villages to forest areas). A particularity of the force of the place would be in their capacity to legitimize the occupation of a specific zone by a population, ensuring its prosperity as well as its attachment to the soil, visà-vis of other local populations in the vicinity.

Photo 2-The village chief places the food on the altar of Choi Noi Cheynam (author, 2010).

In order to see the extent to which we could associate the notion of the force of the place to the phi muang in Khamti society, I will now study the territories associated with them in greater detail, along with their specific relationships and arrangements and their origin, according to them. In addition, the discovery of such a spatial configuration in North-eastern India could be used to provide ethnographic insights into the understanding of the upper part of this region, adding context to the historical sources.

Origin of the phi muangs and their interrelations

Chao Noi Cheynam Among the three phi muang listed during the fieldwork, Chao Noi Cheynam was the one that was most often cited. According to the data collected, its exercised power extended from the Tengapani River to the Noa Dihing River (see Map 1), which currently marks the border between the Lohit and Changlang districts. This area corresponds with the Khamti's original settlement in the region back in the 18th century.

Chao Noi Cheynam literally means "the mountain where the water stagnates", or "the mountain surrounded by water" (in Khamti, noi means "mountain", chey is the verb "to remain" and nam means "water"). In seeking to specify which mountain this referred to, it was found that it corresponded precisely to the Noi Cheynam, and the Khamti questioned affirmed that this mountain was located in the forest of Manabhum, which would thus be the forest that borders their village.

Chow Na Mein (2005), for his part, tells us in his travel account from 2005 that a divinity with similar characteristics is venerated in Myanmar. In the Putao region (in Myanmar), he reported that the Khamti referred to the "noi si nam" (Shan terminology), the mountain ranges that marked the natural border between India and Myanmar. According to the information he collected, Noi Si Nam corresponded with the path taken by the Khamti at the time of their migration to India. During the crossing of this pass, they would have sacrificed a rooster and a hen of red colour 18 .

Historical elements from prior to the arrival of the Khamti in India can shed light on the sacred character of this mountainous area. Before the arrival of the Ahom and Khamti, Upper Assam was dominated by the Chutiya kingdom (religious language). These were divided into four clans, one of which was the Tengapanyas, who lived along the Tengapani River (now the Lohit District). Sidney [START_REF] Endle | The Kacharis[END_REF][START_REF] Endle | The Kacharis[END_REF]) reported that this clan had observed a cult on a mountain in Manabhum. He also reported that this forest coincided with the location of an older cult, which was practiced by the Deori population, one that was now assimilated with the Chutiya population. According to an informant I met in Tinsukia in 2010, there was also an Assamese work that described how when the Khamti settled along the Lohit River, they persecuted the Deori, asking them to close and then move this place of worship. This concordance of places made it possible to suppose that the Khamti, which were occupying the district of Lohit due to their migration in the North-East, would have taken their account of the cult of Deori and transformed it into that of Noi Cheynam, since the natural surrounding lends itself to it 19 . The physical characteristics of the middle of the Putao region (Upper Myanmar) and those of the Lohit district in Arunachal Pradesh are also identical, and the district of Lohit is composed of hills and many rivers. This hypothesis is thus all the more likely as, during our stay in the region, violent incidents would break out between the Deori populations living in the village of Mahadevpur, which marks the current border with the State of Assam, and the Khamti. The Deori were also refused access to the forest of Manabhum, even though they wanted to celebrate an ancient ritual there 20 .

Chao Noi Tipam

The second phi muang is Chao Noi Tipam. During the fieldwork, the Khamti that were interviewed agreed to define its territory from the Noa Dihing River, on the south bank of the Brahmaputra. Unlike the Chao Noi Cheynam, it was difficult for me to obtain precise data on the origin of Noi Tipam from my Khamti informants. Other sources, mainly Indian scholars, were used to help in the defining of its origin.

To this point, we know that it is a male spirit, as the term "noi" refers to a mountain or mountain range with which the divinity would be associated. In his volume on the toponymy of Assam, the Indian historian [START_REF] Phukan | Toponymy of Assam[END_REF] reminded us that Tipam is a Tibeto-Burmese term that can be translated in different ways ("ti" means water, river; "pam", place).

Digging further into the history of the region, the term Tipam refers to several localities and several events that took place during the medieval period, i.e. from the arrival of Ahom in the 13th century until the advent of the British who eventually took root in the region in 1826.

During this time, the name Tipam first corresponded with a small kingdom in Upper Assam that existed at the time of the migration of the first Shan, the Ahom in the 13th century. In his voluminous history of the different Tai kingdoms, [START_REF] Gogoi | The Tai and the Tai Kingdoms. With a Fuller Treatment of the Tai-Ahom Kingdom in the Brahmaputra Valley[END_REF] mentioned that when the first Ahom ruler, Sukapha, settled in the region, he first conquered the kingdom of Tipam, which was located along the Burhi Dihing River, and whose inhabitants were called the Tipamia. This kingdom was then the vassal of the Chutiya (the most important kingdom in upper Assam), which was under the control of a Tai prince named Samlonhpha. Gogoi added that after a consultation with the latter and seeing Sukapha's intention to settle permanently in the region, Samlonhpha decided to offer him the territory of Tipam. Quoting Dheodai Buranji, Gogoi said that Sukapha initially stayed in Tipam for three years, during which he established his first capital city 21 . However, having become aware of the numerous floods in the area that occurred during the monsoon, he settled further north, in the village of Halaguri, near the river Lohit. Indeed, the lowlands in which the kingdom of Tipam was located were not suitable for irrigated rice cultivation. Ahom Buranji (the main historical chronicle from the Ahom period) further stated that the fragility of the soil did not allow the construction of barricades in the new capital, which prevented it from protecting itself (Barua 1985, 46). Thus, during the history of the region, Tipam was a witness to many wars 22 . Today, Tipam is the name of two localities in Upper Assam located in the Dibrugarh district: Tipam Phake and Tipamia. These two localities are included in the protected area by the divinity associated with Noi Tipam. The first is located a few kilometres from the town of Jaypur. [START_REF] Thakur | The Tai Phake of Assam[END_REF] reported that, according to the inhabitants of this village, the Phake, which was close to the Khamti, settled on the north bank of the Burhi Dihing River. At that time, they worshipped the deity Somdeo, who required an annual sacrifice of a buffalo. The Phakes would then choose a place a few kilometres from the temple that was dedicated to Somdeo, where they would keep the buffalos before sacrificing them. Furthermore, Thakur informs us that in the Tai-phake language, "ti" means place and "pling" keep. Thus, before becoming Tipam, this locality would have been called Tipling, "place where one keeps

[buffaloes]" (Takhur 1982, 22). This interpretation, gives Tipam's name a sacrificial value, is close to the contemporary meaning given to it by the Khamti.

The second locality, Tipamia, is further upstream, along the Bhuri Dihing River. Today, this village is best known to be in Upper Assam, as the home of an important Buddhist monastery. While it is not possible to locate the original location of the place of worship dedicated to Tipam, the presence of this monastery allows us to hypothesize that this place of worship was built in place of the original thaan (sacred place) which was dedicated to the Chao Noi Tipam.

Nang Hoo Toungh

Towards the north of the Lohit River is the Nang Hoo Toungh territory 23 . The third phi muang is, as the prefix "nang" (lady) indicates, a female divinity. The territory it is said to protect is more easily identifiable than that of the two-previous phi muangs. Nang Hoo Toungh is known in Assamese as Kesakhati ("person who eats raw meat"). A famous temple bears her name in Upper Assam, and it is dedicated to Tamreswari, nesting on the banks of the Brahmaputra River, which just a few kilometres from the town of Sadiya. However, the current location of this temple does not correspond with the original location of the temple, which is probably located on a hill. Due to numerous earthquakes, it was destroyed, and then rebuilt several times on the plains, leading to its current site along the Brahmaputra.

In the writings pertaining to the history of the Assam, the temple of Kesakhati is also noted to be associated with the Chutiya, whose kingdom was annexed by the Ahom in the early sixteenth century. This temple has the specificity of having a copper roof (tamar, in Assamese, means "copper"). This intrigued the English during the colonial period, and François [START_REF] Jacquesson | Abrégé d'Histoire de l'Assam jusqu'à l'installation anglaise[END_REF] recalled that human sacrifices were made there every year until the beginning of the 19th century. These sacrifices were used to appease the anger of the goddess, which is in the form of Kali. [START_REF] Kakati | The Mother Goddess Kamakhya. Gauhati: Lawyer's Book Stall[END_REF] informed us that the officiants of the goddess were of Deori descent (Kakati 1967, 62). [START_REF] Barua | Temples and Legends of Assam[END_REF], referring to [START_REF] Kakati | The Mother Goddess Kamakhya. Gauhati: Lawyer's Book Stall[END_REF], indicated that it was the most important temple in Upper Assam, and that many people worshipped Tamreswari and participated in human sacrifices. Terwiel also stated that during his investigation, the Khamyang of Chalapathar village had told him that in the past, they also worshiped a female deity, Nang Hua Tong (Khamyang terminology). Following [START_REF] Gait | A History of Assam. Gauhati: Lawyer's bookstall Gogoi[END_REF], Terwiel began to associate this divinity with Tamreswari. He noted that the Khamyang worshipped the goddess twice a year, after the Sangkhen festival (Buddhist New Year) and at the time of the rice harvest in October. However, he pointed out that in the 1980s, the sacrifice offered to Nang Hua Tong was replaced by a Buddhist practice which consisted of the construction of a sand pyramid called cetii kong mu (Kondinya 1986, 31). It is interesting to note that the construction of these pyramids also coincided with the sacred days (wan kam 24 , in Tai-khamyang, equivalent to satangs for the Khamti) in which the sacrifices were offered to the goddess (Terwiel 1981, 31). In other words, the bi-annual sacrifice was thus replaced by the construction of pyramid during the designated holy days. As is the case found in other Tai populations, these holidays take place on the 8th and 15th days of the rising and falling moons.

The elements presented above thus let us suppose that the original temple associated with Tamreswari would correspond with the third phi muang which is venerated by the Khamti, i.e.

Nang Hoo Toungh.

Interrelations between the three phi muangs

The three phi muangs are related to each other. According to the Khamti, a sibling relationship might even exist between these three protective divinities, with Noi Cheynam being the oldest of the three. Indeed, the age of the different divinities makes it possible to show the precedence of one entity (and starting from the territory and the inhabitants it protects) over the others.

In connection with the Buddhist doctrine, and unlike the other two phi muang, Chao Noi Cheynam follows the precepts at an advanced level when compared to the others. This would be at a level of eight moral principles (astha sila). This is the reason why the Khamti offered him a cooked dish, as compared to a raw one, unlike the other two phi muang, which only follow the precepts associated with the laity, totalling five in number.

It has already been mentioned that during the Khamti migration, the Chutiya kingdom occupied the Lohit region. In his work, the Reverend [START_REF] Endle | The Kacharis[END_REF] had pointed out that each of the four clans worshipped specific divinities which were specific to their respective location.

Each of these divinities reigned over the territory on which one clan or another lived. Girasigira was associated with the Dibongiya clan, Pisha-dema with the Tengapanya clan, and Pishashi-deman (the suffix "shi" is the mark of the feminine, this divinity would be "the daughter") was the divinity of highest importance for the Borgonyia. In addition, Endle did not provide information on the divinity of the Patargoniya (he simply stated that this clan quickly disappeared). Above these four primordial divinities, Endle signalled the existence of a supreme divinity, Kundil Mama. For all these divinities, a Thai had been consecrated. This would be the place where one came to celebrate the divinity annually, and to ask him for protection 25 . In accordance with the information collected with regards to the kinship ties between the three phi muang worshipped by the Khamti, Reverend Endle (1993) wrote that the divinities of each of the Chutiya clans also presented kinship ties.

Moreover, in his thesis on the Dibongyia clan, the Indian historian [START_REF] Saikia | The Dibongiyas. Social and Religious Life of a Priesty Community[END_REF] informed us that Pisa Dema (also known as Boliababa in assamese) and Pisasi Dema (the equivalent of Tamreswari in Assamese) were the children of Kundil Mama. If we were to now postpone the delimitation of the territory of the deities Boliababa and Tameswari with two of the current phi muang, Nang Hoo Toungh and Chao Noi Tipam, we would be able to note a correspondence pertaining to the places of worship. Based on this, one could therefore hypothesize that Nang Hoo Toungh and Chao Noi Tipam corresponds to divinities formerly venerated by the Deori. The Khamti would then have appropriated them during their implantation into the region. Moreover, with regards to these two divinities, the names given by the Khamti and their characteristics-one male and one female divinity sharing sibling relations-correspond to the divine entities that were pre-existing to their arrival (Pisasi Dema or Tamreswari for Nang Hoo Toungh, Boliababa for Chao Noi Tipam). Concerning the origin of the name Chao Noi Cheynam, while its territory corresponds to that of an ancient divinity present in the region, it would seem to be a divinity that can be properly traced to the Khamti. The latter may appear to have taken this name due to the similarity of the natural environment between Upper Myanmar and Upper Assam. The map below shows the information derived from our analyses on the territory of each of the three phi muang, according to the Khamti.

Rivers or streams mark the boundaries of a territory.

Conclusion

Acting as guardian protector unfolding at several levels on which it control the entire living beings, the investigation conducted here on the origin and interrelation of each of the phi muang, along with the characteristics of individual and collective ceremonies, allow us to consider these divinities as forces of place.

In addition, it allows the formulation of certain hypotheses related to their integration and appropriation of the North-East space. The concordances with several local cults and deities that exists prior to their arrival allows us to suppose a transposition of local cults with existing deities in their former place of residence (in present-day Myanmar), such as Chao Noi Cheynam; or by transforming them by "Taiizing", as is the case for Nang Hoo Toung and Chao Noi Tipam.

The territories of each phi muang reveal indeed a particular representation of the northeastern Indian space, and it should also be noted that the territory of each of these divinities do not extend south of the alluvial plain of the Brahmaputra, but rather concentrated on the Upper Assam. During the investigation, no informants were able to cite other phi muang, or even name the divinities residing beyond the areas reported on the map. Moreover, the territorial boundaries of the three phi muang corresponded to the limit of the historical settlement of the Khamti in the region; these could either be inhabited by the different waves of Khamti population or assimilated since the middle of the 18th century. However, it would be prudent to remember that the Khamti have always lived in Upper-Assam historically, and have entrenched themselves in the present-day Namsai district following an agreement with the British officer Hannay in 1843, which occurred after an insurrection that was overthrown by the British power of that time. Since this treaty, which marks a commitment to good conduct, the Khamti have been allowed to relocate along the Tengapani River, where they were originally settled when they migrated towards India.

It should also be noticed that this appropriation of land and social space was not expounded upon according to a concentric model, by circles of power-from the village to a given territory, then to the nation-state scale, where a divinity controls different levels of space -as is the case for many Tai populations who have a nation-state across Southeast Asia.

As for the appropriation of the venerated cults that were present prior to their arrival, we were able to note that up till today, the Khamti were still in conflict with the descendants of the Deori, with whom they refused to give access to the forest of Manahbhum to perform the practices of their old cult. It can thus be assumed that it is by transposing and appropriating preexisting divinities that the Khamti sought to legitimize their presence in the region. The adoption of local deities, which implies their pacification, also includes a desire to pacify the forces of the place to be able to occupy it, thereby legitimizing their presence in Northeast India.

Across South and Southeast Asia, the controlling of a territory by controlling the strength of a place remains a strategy that is often used to legitimize the presence of a group on in any given territory.

1 The Khamti are a Tai speaking people, which is a language largely spread across Southeast Asia. Among the numerous Tai groups and language speakers, the Khamti are classified into the Shan language subgroup (from Tai-Kadai family), also called Tai Long or Tai Yong (or 'Greater Tai'). 2 This area remains the most important Khamti population centres in the country. In Upper Assam, small pockets of Khamti populations and other Tai (Tai Phakey, Tai Ahom or Tai Khamyang) still live in Sivsagar, Tinsukia, and Lakhimpur Districts [START_REF] Gogoi | Tai of Northeast India[END_REF]. In mainland Southeast Asia, Shan people are found in the Northwest of Thailand (Tannenbaum, 2001), and in the Yunnan Province of China, but are mainly in present-day Kachin and Kyin States of Myanmar [START_REF] Robinne | Fils et maîtres du Lac. Relations interethniques dans l'État Shan de Birmanie[END_REF][START_REF] Conway | The Shan Culture, Art and Craft[END_REF]). 3 For more information about the development, growth and collapse of the timber industry in the area, see Lainé 2012. 4 The British saw in the practice of Theravada Buddhism and what it implies, notably the existence of an alphabet (pali) and a morality, as the index of a certain degree of "civilization" of the Khamti, unlike the other populations of the region, notably the Mishmi and the Singphos. Since colonial times, most studies of the Khamti or their religion have focused solely on this aspect of their religious system (see among others [START_REF] Kondinya | Monastic buddhism among the Khamtis of Arunachal[END_REF][START_REF] Pandey | Buddhism and Khamtis[END_REF]. While only a few contemporary authors have reported the presence of a spirit cult (Barua, 1976;[START_REF] Behera | Religious Syncretism: The Change and Continuity. A Study with Reference to Bhuddist Tradition[END_REF], Nathalang ( 2009) recently (re)affirmed that Theravada Buddhism was the only religion of the Khamti. However, she notes that it is by putting their adhesion to Theravada Buddhism at the forefront of their identity that the Khamti today can claim a renewal of Shan identity. 5 In this article, I use the term Tai here to distinguish tai-speaking populations that originate from Thailand (referred to as "Thai"). The term Shan corresponds to a linguistic sub-branch of these Taï populations, to which the Khamti and Ahom belong to, in particular. 6 Early research on Theravada Buddhism stressed dichotomy, while [START_REF] Spiro | Burmese Supernaturalism[END_REF] During this period, I benefited from an appointment offered by the French Embassy at IIT Guwahati to conduct several field trips in Arunachal Pradesh. These amounted to 14 months among the Khamtis. During my visits, I mainly used participant observation and semi-directed interviews, with the help of a field assistant. 8 Writings from the colonial period attest to the presence of many elephants in Khamti villages. During those times, the sale of elephants allowed privileged relations to be maintained with the dominant British power. The latter also granted specific statuses to the Khamti by exempting them from taxes concerning the capture of elephants (Gogoi, 1971, XLI). Furthermore, the writings of Milroy (1922) and [START_REF] Sanderson | Thirteen Years Among The Wild Beasts Of India: Their Haunts And Habits From Personal Observation With An Account Of The Modes Of Capturing And Taming Elephants[END_REF], both important figures in British elephant management, highlighted their knowledge regarding a pachyderm's capture. From the time of the country's independence, elephants became essential for logging, an activity that drove the region's economic development until the end of the 20th century. However, this momentum was stopped by a sudden ban of this activity enacted by the Indian Supreme Court in 1996, which consequently lead to the economic and social disintegration of not only the Khamti society but also for the sale of many pachyderms 9 As a seasonal activity, catches generally begin after the monsoon period at the time of Durga puja (in September/October, this is a date that has been introduced during the British period) and extends until the Buddhist New Year Poi Shangken. This period precedes the arrival of the rains and the beginning of the sowing of rice, which would require labour and therefore need the men in the villages to be available. 10 Among these ritual practices and beliefs would be the consultations of horoscopes that are used to set the date and direction of departure, the chao pling chang ritual exchange ceremony (literally the one that deals with wild elephants) in the forest, or the alliance with Utingna, which is considered the lord of wild elephants [START_REF] Lainé | Vivre et travailler avec les éléphants : une option durable pour la protection et la conservation de l'espèce. Enquête sur les relations entre les Khamti et les éléphants dans le nord-est de l'Inde[END_REF]. Let us add that at the end of the fieldwork, it would appear that each capturer met had his own practices, beliefs, and personal experiences. Thus, unlike the customary ritual of the Khmer, as studied by the French historian Jean [START_REF] Ellul | Le coutumier rituel des capteurs d'éléphants de l'Ouest du Cambodge[END_REF], there are no sets of strictly defined rules on the practices to be performed among the Khamti prior to the capturing of elephants, which is called tranam.

Khamti phandi considers Utingna to be the lord and the king of wild forest elephants. He is represented as a man sitting on an elephant, playing a musical instrument that is described as a flute or lyre (see [START_REF] Lainé | Pratiques vocales et dressage animal. Les mélodies huchées des Khamtis à leurs éléphants[END_REF].

12 For an exhaustive account of elephant catching operations as practised by the Khamti, see Lainé 2014. 13 The term 'phandi' is a neologism that refers to the Hindi term 'phand', which means 'rope'. Literally, the phandi refers to the person who launches the rope used for the lassoing of the elephants. 14 Regarding the presence of pang suea muang on the outskirts of villages, it should be noted that many Khamti also use the Assamese term dangarya baba to describe the altars that are located on the fringes of villages. The Assamese adjective Dangor means great; Dangarya is a term used when one addresses the elderly and baba is a rather affectionate term employed to designate a relative or wise person, such as a sadhu in India. By this definition, dangarya baba can be likened to phi muang. 15 A catching expedition lasts for at least two or three weeks. 16 For example, in Northwest Thailand, Nicola Tannenbaum wrote that in addition to the altar that is dedicated to the spirit phi muang, there is another altar in the village centre, which is called the Tsau Waan (Tannenbaum, 1992). Among the populations within this region, the villages are also repaired annually. This practice is associated directly and solely with Buddhism. Monks are called in to chant mantras to repel evil village spirits (phi hai). Among the Khamti, such purely Buddhist ceremonies exist, despite not being performed annually. They take place only when several calamities happen within the village, such as a series of deaths or crop failures. From memory, the inhabitants of Jenglai has mentioned to me during my research that this ceremony was last held in the year 2000. At that time, the village was closed to outsiders, and as many as seven monks took part in the ceremony. 17 Two Khamti women, both of whom were among the eldest in the village, informed me that in the past, there was a second annual ritual to thank the phi muang during harvest time. Today, the ceremony in honour of the phi muang takes place only once a year, as aforementioned. 18 The practice of sacrificing when crossing a pass is common with other Shan too. The Ahom, when they had migrated to the North-East, had also immolated a rooster during crossing the mountain pass, which opened the plain of Assam to them. They had baptized this mountain Mount Patkai (from "pat", meaning to cut, and "kai", hen). This name is still used today (Jacquesson 2000;[START_REF] Terwiel | Tai of Assam: Sacrifices and time reckoning[END_REF]). 19 Such appropriation of cults from other populations is not uncommon among the Tai in other part of the peninsula. For examples, see [START_REF] Archaimbault | 1971 -The New Year Ceremony at Basak (South Laos), with an afterword by Prince Boun Oum, abridged translation[END_REF] on Tai in Laos. 20 During the investigation, there was difficulty obtaining the recognition of the existence of cults carried out by the Deori in the forest of Manabhum from the Khamti, although many admit hesitantly that there were yearly pilgrimages towards this forest. During the course of the fieldwork, this issue raised important political questions, revealing inter-community tensions in the district. Indeed, recognizing an ancient cult rendered by the Deori in the Manabhum forest would amount to attesting to their previous presence on the territory, which would legitimize the Deori's claim on an autochthony in order to access land rights (which they do not currently have). This is what happened in 2010, during my time in the field. Several members of the Deori community living in Mahadevpur on the border between Assam and Arunachal Pradesh organized a march to demand their Permanent Residential Status (PRS) from the authorities. This march resulted in violent clashes in Namsai (see <http://www.telegraphindia.com/1101024/jsp/northeast/story_13092850.jsp>). 21 The Dheodai Buranji ascribes this area to be near the current villages of Jaypur and Nam-Phake, along the Brahmaputra River). 22 This was the case in 1401, between the Taï Nora and the Ahom; later, in 1563, between the Chutya and the Ahom. During the period of the Mughal wars (17th century), Tipam remained famous as the place where a peace treaty was signed in 1663. During the last period of the Ahom dynasty, in 1768, the inhabitants of Tipam joined the Ahom to suppress the first Moran insurrections, which led to the Moamaria revolution that heralded the decline of the Ahom Empire (see Phukan 2001, 286-288). Finally, from a geological point of view, there is a mountain range called the Tipam Hills (or Tipam series), which crosses the south of the North-East and has an altitude that varies between 2,500 and 4,000 meters. This range lies in the Arakan Valley in Myanmar, extending into the Tripura and extending along the Cachar Hills and Naga Hills in Upper Assam to the border between Assam and Arunachal Pradesh (see Goswami 1960, 97-100). This range contains many deposits, especially sandstone and salt, which was exploited at that time by the Naga (nearby) and the Kachari. 23 Terwiel translates this name as "the lady with the golden head". However, he specifies that it is not about gold but about an alloy of 5 metals that is of the colour gold [START_REF] Terwiel | Tai of Assam: Sacrifices and time reckoning[END_REF]. 24 Wan Kam are days dedicated to Buddhist religious activities. The village must be closed to foreigners during this period, and the inhabitants must not leave the village. On these days, no agricultural or forestry activity can be undertaken. 25 It remains impossible today to find the initial location of each of these thaan, due to the many earthquakes, floods and landslides that have occurred in the region since that time. All of these locations have thus been demolished and rebuilt several times in different locales.

Map 1 .

 1 Map showing the spatial representation of the three phi muangs.

  marked a clear distinction between Buddhism and what he called "supernaturalism" (spirit worship) in Myanmar. Most recent research (like Tannenbaum's work in Thailand in 2001), considers Buddhist and animist (spirit cult practices) as both belonging to the same religious system. 7 The data's presented in this article have been collected between the years of 2008 and 2010.


Georges Mykoniatis
email: georges.mykoniatis@enac.fr

Stephane Puechmorel
email: stephane.puechmorel@enac.fr

Felix Moracamino
email: felix.moracamino@enac.fr

Leila Zerrouki
email: leila.zerrouki@eurocontrol.int

Marcel Richard
email: marcel.richard@neometsys.fr

DEMAND CAPACITY BALANCING IN MULTI-MODAL TRANSPORTATION THROUGH OPTIMIZATION AND SIMULATION

Keywords: Modal shift, Climate change, Greenhouse gas emissions, Short-haul flight, Train, Aviation Travel time, network manager, multi-modality, Demand Capacity Balancing, Air Traffic Management

. An optimal equilibrium point can then be reached through a clever choice of penalties incurred by flying at departure times adversely impacting congestion. Alternative routes may also be considered in the planning, as for a whole category of customers price tag is more important than travel time. However, taking into account that for short haul flights alternative means of transportation may be a viable option, DCB can be addressed in a wider scope by considering surface vehicles along aircraft. A side effect of this holistic approach is the ability to cope with disruptive events. The present work describes a simulation and optimization model tailored to this particular problem.

INTRODUCTION

According to the forecast, by 2040 traffic in Europe is expected to grow over 16.2 million flights in the Regulation and Growth scenario (most-likely) (European Aviation in 2040 Challenges of Growth -Eurocontrol [START_REF]European Aviation in 2040 Challenges of Growth -EUROCONTROL[END_REF]). The estimated traffic growth will create a demand that require to efficiently use tall he available capacity. The result will be a pressure on airport capacity and will have an impact on the global network performance and will certainly reduce the means to cope with contingency. With this future level of congestion, it will become difficult to accommodate minor deviations from plan, and delays will begin to accumulate rapidly.

But the delays and the cancellations have already an important impact on network operations, in 2018, the share of reactionary delay was 46% of total delays, contributing 8.2 minutes per flight. Reactionary delays are generated as a result of an aircraft's late arrival from a previous flight which in turn affects the punctuality of its next flight with the same aircraft, as well as potentially delaying connecting passengers. Subsequently there are two types of reactionary delays: firstly, as a result of the same aircraft being delayed on its next flight (rotational delay) and secondly when another aircraft is delayed as a result of another aircraft typically through passengers, crew and load connection (non-rotational delays) (Eurocontrol CODA 2018 [START_REF]All-Causes Delay and Cancellations to air transport[END_REF]).

Since 2013, there has been an 80% increase in delays attributable to weather. But the weather is not the only cause of disruptions, the example of the 2010 eruptions at Eyjafjallajökull in Iceland which, although relatively small for volcanic eruptions, caused enormous disruption to air travel across western and northern Europe is one of them. There is also Industrial action; Armed conflict; Security incidents; Nuclear accident; Staff shortages; Social movement, Staff shortages; Uncontrolled re-entry of satellites (https://www.eurocontrol.int/articles/disruptions-and-crisis-management) .

The demand capacity balancing is addressed actually by the Air National Service Providers by adaptation of the services on part of the airspace set in various predefined configurations based on volumes called sectors and also functional sectors (the functional sectors allow the allocation of the traffic to a groups of controllers according to the type of operation, e.g. Departure, Arrivals). The airports also have published capacities for the Landing and take-off that could vary according to the meteorological or operational constraints. The network manager is issuing regulation according to the published setting of the airspace and airports, taking into account their relevant declared capacity by the Air National Service Providers (ANSPs) [START_REF]An Introduction to the EUROCONTROL Network Manager Operations Centre -January 2019 -EUROCONTROL[END_REF].

But Air Transportation has to face also the environment challenge. The aviation sector is responsible of 6% of the CO3 emissions (IEA, 2018 [START_REF]CO2 Emissions Statistics[END_REF]), and the air traffic growth significantly more than 4% per year (Airbus Global Market Forecast 2018-2037 [START_REF] Networks | [END_REF]). The IPCC special report 2018 [7] is calling for drastic reductions of greenhouse gas emissions in order to limit warming to 1.5° above pre-industrial levels.

For a distance less than 1500 km, short haul flights ( Eurocontrol defintition: airport-to-airport distance is less than or equal to 1500 km [START_REF]Glossary for Flight Statistics & Forecasts accessed 23[END_REF]) the alternative of another transportation mode could be consider (Follmer et

al. (2008) [9]).

A recent study for Finland by Stefan Baumeister 2019 [START_REF] Baumeister | Replacing short-haul flights with land-based transportation modes to reduce greenhouse gas emissions: The case of Finland[END_REF] showed that replacing short-haul flights could significantly reduce country's transportation climate impact. Furthermore, they found that existing land-based transportation modes can keep up with the travel times of aircraft on routes up to 400 km.

But replacing short-haul flights by ground transportation could not be the way to face the demand in term of transportation for the coming years. The existing ground transportation infrastructures are already facing problem of saturation in the cities and between the cities. Our approach here will not address these critical points.

Our approach is to address the demand capacity balancing by modeling an extended network of operation including air and ground connections. The alternative of ground transportation will only be focused on the short haul (less than 1500 km). This study proposes to address Demand Capacity Balancing by taking into account that for short haul flights alternative means of transportation may be a viable option. The DCB is then addressed in a wider scope by considering surface vehicles along aircraft.

The following scenarios are compared:

1) Full Aviation Solution 2) Short-hauls replaced by ground transportation 3) Full air and ground (less than 1500km) network operation 4) Disruption management with various usecases Our analysis will be based on the real travel time estimation, emissions estimation and cost of operation.

We will keep the definition and values given by Stefan Baumeister 2019 [START_REF] Baumeister | Replacing short-haul flights with land-based transportation modes to reduce greenhouse gas emissions: The case of Finland[END_REF] for the real travel time (RTT) from door to door.

The role of the regional airports could be crucial in the coming years in term of offering potential opportunities to face the demand/capacity challenge. It will be addressed in our approach in one of the uses cases to face the disruptions. The usage of a management tool to help in the collaboration decision making could be envisaged in future works and will take benefits of what have been done on the OPTIMODE project [START_REF] Jung | Simulating a multi-airport Region to foster Individual Door-to_door Travel[END_REF].

The work will be performed by using the Pi-rat Simulator of ENAC which allows to simulate a large amount of flights and evaluate their time of flight and the emissions. The simulation is using the Base of Aircraft Data (BADA) is an Aircraft Performance Model (APM) developed and maintained by Eurocontrol [12].

The ground transportation part will be modelled and introduced in the Pi-rat simulator.

REAL TRAVEL TIME (RTT) MODEL

The real Travel time should take into account the time from the city to the airport, the time in the airport to perform the checking and reach the gate, the time of flight, the connection time between two flights, the time for collecting luggage, crossing the customs and finally the time between the airport and the city.

ADOPTED HYPOTHESES:

Passenger departing from a given airport

We consider as average time from city center to airport of 45mn but usually in Europe the passengers take a buffer for the connection of about 15mn, that gives 1H.

We consider arriving 30min before check-in closes and usually it closes 45 mn before departure time which should allow passengers enough time to clear security and reach the departure gate in time.

That gives: 60+30+45= 2h15mn as Real time from Door to Gate Passenger making a connection in a given airport:

The average connection time that we will consider is 45 mn (time of connection between the two flights or between a flight and ground transport).

Passenger arriving at a given airport:

We consider that average time to go out of the aircraft, claim baggage, cross customs is of 40mn.

Plus, then the time from the airport to the city which is could be an average of 45mn.

That gives for a passenger in an arrival airport a Real time of 1h15mn from aircraft to door.

DEMAND MODELLING

For addressing the demand issue, we will consider one day of operation in Europe based on the flight plan information collected form the Demand Data Repository of Eurocontrol https://www.eurocontrol.int/ddr.

For all the flights we will consider a given aircraft load factor depending of the city pair: departure and arrival.

The difficulty is to estimate the number of passengers making a rotation in a given airport.

The Demand modeling should take into account the passengers' expectations, in term of traveling time, arrival time, and also type of transportation. Several studies based on passenger's centric transportation have been done, [START_REF] Borken-Kleefeld | Mode, load, and specific climate impact from passenger trips[END_REF] and it is difficult to address this issue.

Our approach here is to suppose that we have a distribution of the passenger demand that could be extrapolated on our knowledge of the air transportation figures.

The demand modelling should take into account its increase in the coming years and should consider that the air network and ground network could be close to be saturated. The assumption, that we are taken here is to consider that the initial demand is based on the assumption of the existing today air traffic filled at 87% (about the figures of today for Air France https://fr.statista.com/statistiques/495354/air-france-klm-coefficientoccupation-sieges/ ).

This initial demand will allow to give figures by city pairs and then an extrapolation is performed with the assumption of an increase of 4% per year (figure also coming from the Aviation domain [START_REF]Annual Report 2017, Presentation of 2017 Air Transport Statistical Re-sults accessed 25[END_REF]). This approach has the restriction to not take into account possible evolution of the actual capacity of the network, these could be addressed in future work by modeling the evolution of its capacity.

The various scenarios will be run with a different demand schemes: the initial, the 5 years forecast and the 10 years forecast.

COST OF OPERATION AND EMISSION MODEL

The model for the cost of operation and emission is based on a value per hour of flight according to the type of aircraft and the weight factor for the fuel consumption.

For ground transportation an amount per hour will be taken as basis for the emission: For the ground cost of operation, it will be based on an average value. The CO2 emmission will use the data provided by the French SNCF: https://www.oui.sncf/aide/calcul-desemissions-de-co2-sur-votre-trajet-en-train

EVOLUTIONS OF PI-RAT:

Pi-rat is a fast time simulation tools developed in the premises of the French civil aviation school (ENAC) for the needs of air traffic management research. It is a feature rich tool, based on the well known BADA database from Eurocontrol, and implementing a continuous time point mass model. Weather effects are considered using GRIB meteorological data. A very accurate taxi model along with the ability to simulate UAVs makes it an integrated traffic simulation tool.

For the ongoing work on multimodality, a ground transportation module will be developed, using a graph-based approach and dynamic programming to model user's behavior. Optimized cost functions may include value-oftime considerations, as longer but uncongested routes or cheaper means of transportation may be selected instead of the usual time criterion. Finally, randomness has to be added to the system to better model the travel time uncertainties. Implementing on a realistic, large scale basis such a simulation is quite challenging. The surface transportation system cannot be modeled on a per-vehicle basis due to the overwhelming number of mobiles that would be needed. Instead, the original problem is turned into a maximal flow one, which is easier to deal with. In the current implementation, the surface transportation network is a directed graph G(V,E,f) where V is the set of vertices, E the set of edges and + is the capacity function that maps an edge to its maximum available flow. To cope with uncertainties, for any , the value is in fact a random variable with a known distribution and for , and are assumed to be independent.

DEMAND CAPACITY BALANCING

This regulation is performed seven days or more before the day of operation, called the Strategic phase, one day to six days before the day of operations, called the pre-tactical phase and finally on the day of operation, called the tactical phase. The actual algorithm used for addressing the Demand Capacity Balancing in Europe is Computer Assisted Slot Allocation (CASA), but it will evolve in the coming years to address the issue of the Collaborative Air traffic Flow Management (cooperation between airspace users and airspace service providers) and also the environmental concerns. In our case, we selected to use an algorithm described below using a given heuristic but where other greedy heuristics could be proposed, some, through the computation of the environmental impact of each candidate route, or through a trade-off between airlines costs and environmental impact.

The Demand/Capacity algorithm:

Let F be the set of programmed flights for the considered day of operation, then for each programmed flight f i iF, is built from the preferred 4D route, r=1, a set of alternate routes r =2 to R i . These 4D routes are either delayed or lengthened or both to provide a diversity of offers able to overcome, through delay or increased flying costs, congestion situations in air traffic control sectors. An airline additional cost aac ir can be assigned to these routes with c i1 = 0.

The whole considered airspace is subdivided into S air traffic sectors while time is discretized with period of 3 minutes: t k =t 0 + k T, 0  k  K, where t 0 is the opening operations time and K is the number of considered successive periods in a day. At time t k , k{1,…,K}, sector s{1,…,S} is supposed to have a known traffic capacity (measured in number of aircraft) written sc sk .

An incident matrix M can be computed between the (i, r) flights, iF, r{1,…,R i }and the (s,k) sectors, s{1,…,S}, k{1,…,K}, it is given by:

M(i,r,s,k)=1 if route (i,r
) is in sector s at time period k and M(i,r,s,k)=0 otherwise.

Then the Demand Capacity Balancing problem can be formulated as a discrete optimization problem such as:

under the constraints Here the first restriction set, about the binary variable x ir , indicates that only one route will be selected for flight i. The second restriction set indicates that at anytime in any sector, traffic cannot be higher than planned capacity.

The prior generation of all candidate 4D routes for each flight may appear to be a huge task, but it has some important advantages:

-Involve airlines to candidate route set definition, this is someway a collaborative situation.

-Avoid at the solution stage to have to rebuilt 4D trajectories while involved with searching for a global solution.

A greedy heuristic solution can be easily constructed according to the following steps:

1) Rank for each flight the candidate routes by increasing additional airline costs.

2) Start at iteration zero for each flight i with x i1 =1, x ir = 0, r{2,…,R i }, i.e. the preferred route of flight i.

3) Define the set of active routes as A={(i,r): x i1 =1 }.

4) Check if the capacity constraints are satisfied with the current active route set. For that, compute current traffic demand D sk for each sector at all instant: If , the active set is the solution set: End Otherwise proceed to next step.

5) Rank each active route (i,r) in A by decreasing order with respect to its global capacity impact factor  ir given by: where  is a positive parameter. Once the change in the route of flight i* has been performed go back to step 4.

Observations:

-In the improbable case in which no route shift can be performed at step 6, this algorithm fails and the procedure can be restarted with extended candidate route sets, especially for the leading flights of the ordered list of step 5.

-The algorithm can be speed up by shifting more than one route at each iteration (step 6).

-The proposed heuristic presents a unique setting parameter, , which can be taken as a constant or may be changed (increased) during the search process to cope with small excesses of traffic demand.

-The algorithm is compatible with dynamic traffic control sectors.

-The algorithm must be modified slightly to cope with landing and take-off capacities at airports considered as two-way sectors.

-To take into account somehow ground transportation, a fictitious ground sector can be attached to airports to take into account, the ability of ground transportation to tackle departing and arriving passengers in an hourly basis.

-Other greedy heuristics can be proposed, some, through the computation of the environmental impact of each candidate route, can propose a trade-off between airlines costs and environmental impact.

THE SCENARIOS

The network cities to take into account could be just a model as in the study performed by Jung, M. &al , Classen, A.B., Rudolph, F., Pick, M., Noyer , U., [START_REF] Jung | Simulating a multi-airport Region to foster Individual Door-to_door Travel[END_REF] or a given airspace such as the whole European area, the French airspace, a region…

FULL AVIATION SOLUTION

In this scenario, the inputs will be one day of traffic and the analysis will be performed based on city pairs (departure-arrival airport).

SHORT-HAULS REPLACED BY GROUND TRANSPORTATION

For all the short haul, the flight connection is replaced there by a model for the ground transportation. The value taken for the emission will be based on the Thalys figures considered as an average comparatively to other train emission :(TGV : 2,4 g CO2 /km, Thalys : 8,6 g CO2 /km ,Eurostar : 11,45 g CO2 /km, Gala : 8,4 g CO2 /km, Alleo : 9 g CO2 /km: https://www.oui.sncf/aide/calcul-des-emissions-de-co2-sur-votre-trajet-en-train Alternative scenario could be considered in the future with different values for the emission.

DISRUPTION MANAGEMENT WITH VARIOUS USECASES

INTRODUCTION

In our approach only two use cases will be addressed, considering that they are the mains causes of delay in our current operations. Other use cases will be defined in the future such as airspace closure or others.

USECASE WEATHER

For this use case we consider that a part of the airspace will create significant delays for the air transportation. This will be done by a random selection of a group of city pairs in a given area of operation. The delay introduce will vary according to the size of the area of perturbation. In term of emission impact is will be connected to the duration of the flight only not to the evaluation of Gaz emission need to keep the navigability in difficult weather operation.

USECASE AIRPORT CLOSURE

For this use case one of the major hubs is close and the traffic should be diverted to neighboring airports.

CONCLUSIONS

However, taking into account that for short haul flights alternative means of transportation may be a viable option, DCB can be addressed in a wider scope by considering surface vehicles along aircraft.

A side effect of this holistic approach is the ability to cope with disruptive events. The present work describes a simulation and optimization model tailored to this particular problem. It has been addressed by a set of scenarios, use cases and by consideration on the real travel time, emission and cost of operation. The future work will allow to run the scenarios on various type of airspaces and to provide useful conclusions for the new way to approach the demand capacity issues in the coming years.

First A . 6 )

 .6 Author, Second B. Author, and Third C. Coauthor. Choose i* such that (i*,r*) is the first of the above ordered list and do: If r* R i : route (i*,r*) is replaced by route (i*,r*+1) in the active set A.If r*=R i* , flight i* cannot be downgraded, then take the second flight (i**, r**) in the ordered list, reassign indexes i* and r* to route (i**,r**) and restart step 6).

First A .

 . Author, Second B. Author, and Third C. Coauthor.


Rémi Manceau

Hybrid temporal LES: Development and applications

The HTLES approach, based on temporal filtering, is a formally consistent way to hybridize (U)RANS and LES. Recent advances are presented as well as applications using industrial codes, which show the strong potential of this approach for industrial CFD.

Introduction

A rigorous formalism for continuous hybrid RANS/LES methods is highly desirable to favour the modelling of subgrid stresses, comparison with experiments/DNS and understanding of the observed phenomenology. The usual hybrid methods are limited by the fact that statistical averaging (RANS) and spatial filtering (LES) are generally inconsistent [START_REF] Fadai-Ghotbi | Temporal filtering: a consistent formalism for seamless hybrid RANS-LES modeling in inhomogeneous turbulence[END_REF].

Temporal filtering

Generalized temporal filters, characterized by time integration at a moving application point,

U(x, t) = t -∞
G T (t, t )U(ξ(x, t, t ), t ) dt , [START_REF] Fadai-Ghotbi | Temporal filtering: a consistent formalism for seamless hybrid RANS-LES modeling in inhomogeneous turbulence[END_REF] are introduced in order to build a consistent formalism for hybrid methods for stationary, inhomogeneous turbulence, since the time-filtered quantities go to the statically-averaged quantities within the limit of an infinite filter width [START_REF] Fadai-Ghotbi | Temporal filtering: a consistent formalism for seamless hybrid RANS-LES modeling in inhomogeneous turbulence[END_REF]. To satisfy the Galilean invariance, the uniform temporal filter [START_REF] Manceau | Progress in Hybrid Temporal LES[END_REF] is used here, where V ref is an arbitrary velocity. As illustrated by Figure [START_REF] Fadai-Ghotbi | Temporal filtering: a consistent formalism for seamless hybrid RANS-LES modeling in inhomogeneous turbulence[END_REF], the filtering process leads to temporal LES (TLES), URANS or RANS, depending on the cut-off frequency. The phase shift is due to backward-in-time integration (causal filter).

ξ(x, t, t ) = x + (t -t)V ref , (2) 0 -2 -
The equation of the filtered momentum is as follows

∂ U i ∂t + U k ∂ U i ∂x k = - 1 ρ ∂ P ∂x i + ν ∂ 2 U i ∂x j ∂x j - ∂τ ij sfs ∂x j ( 3
)
and the transport equation for the subfilter stress (SFS) tensor τ ij sfs is also formally identical to the RANS equation for the Reynolds-stress tensor u i u j , and tends exactly towards this equation within the limit of an infinite filter width, which forms a solid foundation for the development of hybrid RANS/LES approaches [START_REF] Fadai-Ghotbi | Temporal filtering: a consistent formalism for seamless hybrid RANS-LES modeling in inhomogeneous turbulence[END_REF].

Hybridrization with URANS

For a filter width of the order of magnitude of the integral time scale of turbulence, the filtered velocity only contains large-scale, quasi-periodic oscillations, Figure [START_REF] Fadai-Ghotbi | Temporal filtering: a consistent formalism for seamless hybrid RANS-LES modeling in inhomogeneous turbulence[END_REF], similar to URANS solutions. It can be shown that using this filter width leads to the URANS equations (i.e., the RANS system with time derivative) such that URANS can be regarded as a time-filtered approach [START_REF] Manceau | Progress in Hybrid Temporal LES[END_REF]. As a consequence, the HTLES methodology can also be used to bridge URANS and Temporal LES, which extends the validity of HTLES to non-stationary configurations.

Subfilter stress model

As in the case of standard LES, a closure problem must be addressed due to the presence of the subfilter stresses τ ij sfs in Eq. (3).

Hybridization method

The HTLES approach is based on the introduction of two filters with characteristic frequencies ω c and ω d , Figure [START_REF] Manceau | Progress in Hybrid Temporal LES[END_REF]. Integrating the equation for the Eulerian temporal energy spectrum E T (x, ω) on the ranges [ω c ; ω d ] and [ω d ; ∞[, respectively [START_REF] Fadai-Ghotbi | Temporal filtering: a consistent formalism for seamless hybrid RANS-LES modeling in inhomogeneous turbulence[END_REF], and using a perturbation method to derive the dissipation term [START_REF] Friess | Toward an equivalence criterion for hybrid RANS/LES methods[END_REF], the equation for the subfilter turbulent energy k sfs can be written as follows where P sfs and D sfs are the subfilter parts of production and diffusion. The time scale that determines the dissipation term is

Dk sfs Dt = P sfs + D sfs - k sfs T , (4)
T (r) = r ψ(r) k ε , (5)
where

r = k sfs k ; ψ(r) = 1 + C ε2 C ε1 -1 1 -r C ε1 C ε2
(6) (the overbar denotes Reynolds averaging). The subfilter-to-total turbulent energy ratio r goes to unity at the RANS limit, in which case Eq. ( 4) tends towards the RANS equation. The modified time scale enforces the LES mode for r < 1 by increasing the dissipation term k sfs /T , similar to two-equation DES. This method can be applied to two-equation models ( [START_REF] Tran | A hybrid temporal LES approach. Application to flows around rectangular cylinders[END_REF][START_REF] Afailal | Development and validation of a hybrid temporal LES model in the perspective of applications to internal combustion engines[END_REF][START_REF] Duffal | Development and validation of a hybrid RANS/LES approach based on temporal filtering[END_REF] or to second moment closures, replacing ε in the dissipation tensor with k sfs /T [START_REF] Friess | Toward an equivalence criterion for hybrid RANS/LES methods[END_REF]. Eq. ( 4) bears similarities with the corresponding equation in DES, in which the dissipation term writes k 3/2 sfs /L. However, HTLES also differs significantly from DES: it relies on a modified time scale rather than a length scale; Eq. ( 5) is based on the comparison of averaged quantities (r and k/ε); DES is an empirical approach, without explicit reference to a particular formalism, although it can be interpreted as a simplified version of HTLES [START_REF] Friess | Toward an equivalence criterion for hybrid RANS/LES methods[END_REF].

Switchover criterion

As seen in Eq. ( 5), the criterion that determines the switchover from RANS to LES is the ratio r, which must now be linked to the cutoff frequency ω c . It seems optimal to link the cutoff frequency to the Nyquist frequency related to the time step dt,

ω c = 2π 2dt . ( 7
)
However, for a sufficiently small time step, this frequency cannot be observed in the computation, The small vortex at the bottom generates higher frequencies. However, if the grid is not fine enough, small vortices and their corresponding frequencies are missing, so the maximum observable frequency is

ω c = min π dt ; U s π ∆ = U s π ∆ min 1; ∆ U s dt , ( 8
)
where U s is the sweeping velocity [START_REF] Tennekes | Eulerian and Lagrangian time microscales in isotropic turbulence[END_REF], and U s dt/∆ can be called the sweeping CFL number. The sweeping velocity is U s = U + u, where U is the mean velocity magnitude and u = γ √ k is the characteristic velocity of the energetic eddies, with γ a coefficient usually chosen as unity.

The assumption of an equilibrium Eulerian spectrum [START_REF] Tennekes | Eulerian and Lagrangian time microscales in isotropic turbulence[END_REF]

E T (ω) = C κ ε 2/3 U 2/3 s ω -5/3 , ( 9
) yields r = 1 k ∞ ωc E T (ω) dω = 1 β U s √ k 2/3 ω c k ε -2/3
(10) As usual for hybrid RANS/LES methods, the coefficient β = 0.67 is calibrated in homogeneous isotropic turbulence, so that, as shown in Figure [START_REF] Tran | A hybrid temporal LES approach. Application to flows around rectangular cylinders[END_REF], the decay of energy follows the DNS data.

Note that Eq. ( 10) and Eq. ( 8) actually define a twofold switchover criterion: if the sweeping CFL Figure 5: Hill flow. Q-isosurfaces coloured by the velocity magnitude. Background : ratio r s [START_REF] Duffal | Development and validation of a hybrid RANS/LES approach based on temporal filtering[END_REF].

number is less than one, the switchover criterion is the ratio of the grid step to the integral length scale; otherwise, it is the ratio of the time step to the integral time scale.

Shielding of the near-wall region

One of the main objectives of hybrid approaches is to treat the near-wall region in RANS mode, in order to avoid the unaffordable cost of wall-resolved LES. Fadai-Ghotbi et al. [START_REF] Fadai-Ghotbi | A seamless hybrid RANS/LES model based on transport equations for the subgrid stresses and elliptic blending[END_REF] proposed to shield the near-wall region, an idea that was developed independently for the DDES approach [START_REF] Spalart | A new version of detached-eddy simulation, resistant to ambiguous grid densities[END_REF]. In order to define a shielding function independent of the grid, it is important to base its definition on quantities that are the same in both RANS and LES modes. Duffal et al. [START_REF] Duffal | Development and validation of a hybrid RANS/LES approach based on temporal filtering[END_REF] replaced in Eq. ( 5) and Eq. ( 6) the ratio r by the shielded ratio r s

r s = 1 -f s max[0, 1 -r], (11)
with the shielding function f s

f s = 1 -tanh [ξ p ] where ξ = C L ν 3 /ε 1/4 d w , (12)
and d w is the distance to the wall. The advantage of using the Kolmogorov scale in ξ rather than, for example, the integral scale, is that the dissipation rate ε, obtained from its transport equation, is reasonably independent of the grid, such that the thickness of the shielded region is also gridindependent [START_REF] Duffal | Development and validation of a hybrid RANS/LES approach based on temporal filtering[END_REF].

Another possibility is to use the elliptic-blending parameter α [START_REF] Fadai-Ghotbi | A seamless hybrid RANS/LES model based on transport equations for the subgrid stresses and elliptic blending[END_REF][START_REF] Afailal | Development and validation of a hybrid temporal LES model in the perspective of applications to internal combustion engines[END_REF], solution of

α -L 2 sfs ∇ 2 α = 1, (13)
with α = 0 at the wall and define r s as

r s = (1 -α 2 ) + α 2 r. ( 14
)
Figure 6: Square-sectioned cylinder. Q-isosurfaces coloured by the velocity magnitude [START_REF] Tran | Développement d'une méthode hybride RANS-LES temporelle pour la simulation de sillages d'obstacles cylindriques[END_REF]. Another difficulty is that the shielding does not prevent resolved vortices from penetrating into the near-wall RANS region, Figure [START_REF] Afailal | Development and validation of a hybrid temporal LES model in the perspective of applications to internal combustion engines[END_REF]. In order to avoid double-counting, Duffal et al. [START_REF] Duffal | Development and validation of a hybrid RANS/LES approach based on temporal filtering[END_REF] proposed the internal consistency constraint (ICC), which excludes the resolved energy k r due to these fluctuations from the total turbulent energy by the use of

T = r ψ(r) k sfs + c r k r ε , where c r = 0 if r s = 1, f s if r s < 1. ( 15
)
3 Some Applications

Square-sectioned cylinder

To illustrate the predictive capabilities of the method, the first case is the flow around a squaresectioned cylinder at Re = 21400, computed using Code_Saturne [START_REF] Tran | A hybrid temporal LES approach. Application to flows around rectangular cylinders[END_REF]. Figure [START_REF] Duffal | Development and validation of a hybrid RANS/LES approach based on temporal filtering[END_REF] shows that the flow in the vicinity of the cylinder is smooth and quasi-2D as in URANS computations. In the wake, the model gradually switches to the LES mode. Figure [START_REF] Tennekes | Eulerian and Lagrangian time microscales in isotropic turbulence[END_REF] shows profiles extracted along the symmetry line behind the cylinder. URANS and HTLES are using the same closure, the k-ω-SST model, and the same grid. This figure clearly shows the superiority of HTLES over URANS. The HTLES results are also close to the LES results, although the number of cells is reduced by a factor of 145 (0.5 × 10 6 vs. 72.9 × 10 6 ), because the near-wall region is resolved in URANS mode.

Periodic-Hill Flow

The second case is the periodic hill [START_REF] Breuer | A comparative study of the turbulent flow over a periodic arrangement of smoothly contoured hills[END_REF] at Re b = 10600. Computations are performed with Code_Saturne [START_REF] Duffal | Development and validation of a hybrid RANS/LES approach based on temporal filtering[END_REF], using the hybridized k-ω-SST model. Figure [START_REF] Afailal | Development and validation of a hybrid temporal LES model in the perspective of applications to internal combustion engines[END_REF] displays in the background the ratio r, which indicates that the hybrid model operates in RANS mode close to the two walls and in LES mode elsewhere.

The skin friction coefficient, Figure [START_REF] Fadai-Ghotbi | A seamless hybrid RANS/LES model based on transport equations for the subgrid stresses and elliptic blending[END_REF], is quite well reproduced compared to the results of the refined LES [START_REF] Breuer | A comparative study of the turbulent flow over a periodic arrangement of smoothly contoured hills[END_REF], although the number of grid cells in reduced by a factor of 70. RANS, using the same k-ω-SST closure, is not able to reproduce the correct reattachment length. LES, using the same mesh as for HTLES does not give acceptable Another particularly interesting point is that, as shown in Figure [START_REF] Tran | Développement d'une méthode hybride RANS-LES temporelle pour la simulation de sillages d'obstacles cylindriques[END_REF], HTLES is able to provide information on wall pressure fluctuations at the wall at a CPU cost much lower than LES, with the exception of the highest frequencies, which can be very useful for predicting of unsteady pressure loads and mechanical fatigue in industrial applications.

Steady flow rig

The third case is called the steady flow rig [START_REF] Thobois | Large-Eddy Simulation in IC Engine Geometries[END_REF], Figure [START_REF] Lyn | Laser-Doppler velocimetry study of ensembleaveraged characteristics of the turbulent near wake of a square cylinder[END_REF], which is a simplified in-cylinder flow around a valve with a fixed lift at Re b = 30000, computed using Converge CFD [START_REF] Afailal | Development and validation of a hybrid temporal LES model in the perspective of applications to internal combustion engines[END_REF]. It can be seen in Figure [START_REF] Cao | Large-eddy simulations of flow past a square cylinder using structured and unstructured grids[END_REF] that RANS does not correctly re- produce the black-flow and the radial velocity. On the other hand, HTLES provides results similar to those of LES and is in relatively good agreement with the experiments.

But the most interesting result in favour of the hybrid model is the prediction of the pressure drop given in Table [START_REF] Fadai-Ghotbi | Temporal filtering: a consistent formalism for seamless hybrid RANS-LES modeling in inhomogeneous turbulence[END_REF]. The success of HTLES in this matter compared to LES relies on the use of the RANS mode in the admission pipe and around the valve, where a refined LES would be necessary. This result is probably the best illustration of the main asset of hybrid methods in general, and HTLES in particular: the use of the most appropriate model in each region of the flow.

Conclusion

Temporal filtering provides a consistent formalism for the hybridization of RANS (or URANS) and LES, either for first or second moment closures. The resulting HTLES approach bears some similarities with DES, but migrates from RANS to 1: Steady flow rig. Pressure drop between the inlet pipe and the outlet of the domain [START_REF] Afailal | Development and validation of a hybrid temporal LES model in the perspective of applications to internal combustion engines[END_REF].

LES in a very different way. Recent applications have demonstrated the performance of HTLES, which is able to provide results similar to those of LES, with a drastic cost reduction linked to the use of RANS in the near-wall region. These results also show the potential of hybrid approaches for the prediction of unsteady loads and as a solution to the issue of the prediction of the pressure drop with LES in industrial applications.

Figure 1 :

 1 Figure 1: Synthetic turbulent signal. Application of a top-hat temporal filter with several cutoff frequencies ω c . ω 0 corresponds to the integral scale.

Figure 2 :

 2 Figure 2:Spectral zones of HTLES. Premultiplied energy and dissipation spectra, ω E( ω) and ω D( ω), respectively, in units based on the integral scales.

Figure 3 :

 3 Figure 3: Sweeping mechanism [7].

Figure 4 :

 4 Figure 4: Decaying isotropic turbulence at Re λ = 104.5. Evolution over time of the energy spectrum predicted by HTLES based on the k-ω-SST model [4].

Figure 7 :

 7 Figure 7: Square-sectioned cylinder. Mean (left) and rms (right) streamwise velocities along the axis of symmetry.

Figure 8 :

 8 Figure 8: Hill flow. Distribution of skin friction on the lower wall [6].

Figure 9 :

 9 Figure 9: Hill flow. Streamwise velocity profiles. From Afailal et al. [5].

Figure 10 :

 10 Figure 10: Hill flow. Pressure spectrum at the top of the hill [6].

Figure 11 :

 11 Figure 11: Steady flow rig. HTLES computation. Q-isosurfaces coloured by the velocity magnitude. Only half of the cylinder is shown. From Afailal et al. [5].

Figure 12 :

 12 Figure 12: Steady flow rig. Velocity along a radial line located 5.8D downstream the expansion. Top: axial component. Bottom: radial component. From Afailal et al. [5].

Table

	EXP RANS HTLES LES
	∆P [Pa] 1766	1713	1705	1957
	Error [%]	-3	-3	+11

Acknowledgements

Several colleagues and students have contributed over the years to the progress of time-filtered hybrid RANS/LES approaches. They are listed in alphabetical order: H. Afailal, Ch. Angelberger, J. Borée, V. Duffal, A. Fadai-Ghotbi, Ch. Friess, J. Galpin, T.B. Gatski, B. de Laage de Meux, R. Perrin, T.T. Tran, A. Velghe. The author is indebted to T.T. Tran, V. Duffal and H. Afailal for producing the results and figures presented in section 3. A part of this work was supported by ANR within the framework of the MONACO_2025 project (ANR-17-CE06-0005-01 ACT).