Helene Maisonnave Edehn

Ramos Mabugu
email: rmabugu@gmail.com

Margaret Chitiga
email: margaret.chitiga@gmail.com.

Economywide consequences of attaining Millenium Development Goals in South Africa

South Africa has committed to eliminate poverty and reduce inequality by 2030 in its National Development Plan. To realise this, it will be critical to make strides in attaining the Millennium Development Goals. This paper uses a computable general equilibrium model to show the complexities of trade-offs between attaining these goals and their financing. There are clear spillover benefits from attaining goals such as universal primary education, and combating HIV-AIDS that the model takes into account. The conclusions point to the need for weighing up merits of different policies against their cost.

Introduction

South Africa has committed to eliminate poverty and reduce inequality in the National Development Plan (NDP). To realise this vision by 2030, it will be critical for South Africa to make strides in attaining the Millennium Development Goals (MDGs). With 2015 fast approaching which is the cut-off date for realisation of the goals, it is imperative to ask questions about feasibility of achieving MDGs in South Africa. This paper discusses this question with a focus on the financial requirements of attaining some of the critical MDGs. Specifically, the paper uses a computable general equilibrium (CGE) model to show the spillover effects of achieving health and education MDGs.

Progress in achieving the health-related MDGs has been especially slow in South Africa. Based on current trends, the country will not reach the MDGs for child mortality (Goal 4) and maternal mortality (Goal 5). This paper is one of the first studies of its kind in the region that takes a detailed look at the economic impact of different options for creating and using fiscal space to attain outstanding MDGs. The rest of the paper is arranged as follows, section two discusses the MDG targets and progress in attainment. Section three discusses the model used with a special focus on the MDG module. In section four the results are discussed and section five concludes.

Status of MDG achievement in South Africa

South Africa has made progress in reaching some MDGs. MDG1 (Eradicate extreme poverty and hunger) was achieved in 2011. Indeed, the proportion of people experiencing extreme poverty (those living on less than $1 a day) fell by over half, from 11.3 per cent in 1994 to 4.0 per cent in 2011 (Republic of South Africa, 2013, p.122).

MDG 2 requires that, by 2015, children everywhere, boys and girls alike, will be able to complete a full course of primary schooling. According to [START_REF] Hollenbeck | Education and the Economy[END_REF], educational attainment of individuals may be important on equity grounds, because an individual's education may be the key to their economic situation. Education determines the distribution, not just the growth, of income. Studies conducted in developing countries indicate that maternal schooling is also a very strong and consistent predictor of reduced child mortality and morbidity [START_REF] Pavalavalli | Maternal Education and the Utilization of Maternal and Child Health Services in India[END_REF]. As education can play a major role in attaining equity and health-related goals, education goals are discussed in more depth later. The number of 15 to 24 year olds who are literate has been increasing steadily, from 83.3 per cent in 1994 to 90.7 per cent in 2011 for females and from 88.4 per cent in 1994 to 94.6 per cent in 2011 for males (Republic of South Africa, 2013, p.124). Although South Africa has almost achieved the MDG target on primary education outcome before 2015, issues of educational quality and functionality remain critical within the country.

MDG3 deals with gender equality. The secondary and tertiary Gender Parity Index (GPI) of 1.07:1 and 1.38:1 for 2011 respectively, shows that slightly more girls than boys attend secondary and tertiary schools, indicating that the goal is achieved. However, for primary school, the GPI is at 0.96:1 in 2011, meaning that South Africa is still on track. (Republic of South Africa, 2013, p.125). MDG4 is related to child mortality. Progress in the reduction of child mortality is assessed against three main indicators: under-five mortality rate, the infant mortality rate and the proportion of one-year-old children immunised against measles. Infant mortality declined from 54 in 2001to 53 in 2007(StatsSA, 2008) and to 38 in 2010(Republic of South Africa, 2013). Although progress is in the right direction it is still far from the set target of 18 per 100,000. The high numbers are mainly as a result of HIV/AIDS.

The target for under-five child mortality is set at 20 per 1,000 live births. Between 1993 and 1998, estimated under-five mortality rates were 59 per 1,000 live births. However, this figure has since risen, from 97 in 2001 to 104 per 1,000 live births in 2007 (The Presidency, 2010). South Africa's child mortality is mainly due to the HIV/AIDS pandemic, which is responsible for more than half (57 per cent) of child deaths [START_REF] Hill | Estimates of maternal mortality worldwide between 1990 and 2005: an assessment of available data[END_REF]. South Africa is one of 12 countries in which the child mortality rate has increased instead of fallen since 1990 (Health Systems Trust, 2009). As a result, to meet MDG4, South Africa has to achieve an average yearly rate of reduction of 14 per cent by 2015, which is unlikely to be met (The Presidency, 2010). However, using other data, (Republic of South Africa, 2013), infant mortality fell from 48 to 38 between 2007 and 2010. Against the target of 18, it is still clear that reaching this goal will have to take concerted effort on the part of all stakeholders involved. MDG5 deals with maternal health. The South African maternity mortality rate is increasing, more than doubling between 1998and 2003, from 84.25 to 165.50 (The Presidency, 2008). In 1998, maternal mortality was 150 per 100,000, but increased to 369 in 2000 and 625 by 2007, with the target set at 38 for 2015 (Republic of South Africa, 2013). HIV infections are the key reason why South Africa is unlikely to achieve the MDG target (Health Systems Trust, 2009).

MDG6 deals with AIDS, tuberculosis and malaria. As already stated before, AIDS is quite critical is South Africa. An antenatal survey conducted between 2005 and 2006 shows that the prevalence of HIV and AIDS has declined for most provinces, except for the Free State. The survey also showed that the prevalence between the less than 20 years age group has declined, indicating that new infections have slowed. HIV prevalence among the population aged 15-24 years fell from 9.3 per cent to 8.7 per cent between 2002 and 2008, [START_REF] Shisana | South African national HIV prevalence, incidence, behaviour and communication survey 2008: A turning tide among teenagers?[END_REF]. [START_REF] Shisana | South African National HIV Prevalence, Incidence and Behaviour Survey[END_REF], shows that by 2012, HIV prevalence had increased by 1.2 million people living with HIV compared to 2008. The availability of Anti-Retroviral Treatment was one of the main reasons for longer survival rates [START_REF] Shisana | South African National HIV Prevalence, Incidence and Behaviour Survey[END_REF]. To combat HIV/AIDS, the Department of Health introduced a Comprehensive Plan for HIV/AIDS 2007-2011. The plan includes the provision of voluntary counselling treatment (VCT), preventing mother-to-child transmission treatment, nutritional supplementation and antiretroviral treatment to patients infected with HIV and AIDS (UNDP, 2007).

Target 8 of Goal 6 is that South Africa will have halted the incidence of malaria by 2015 and have begun to reverse this and other major diseases. Between 2000 and 2010, the incidence of malaria fell from 64,622 to 8,066 cases and to 6,846 cases by 2012 (Republic of South Africa, 2013). Death rates associated with malaria also fell, from 459 in 2000 to 87 in 2010 to 72 in 2012 against a target of 229, (Republic of South Africa, 2013). This means this target has already been achieved. MDG 7 deals with environmental sustainability. South Africa has become increasingly more committed to improving environmental sustainability. Conservation efforts currently focus on improving biodiversity, expanding protected areas in hot spots, establishing Transfrontier Conservation Areas with neighbouring countries and establishing cross-sectoral programmes that focus on development and poverty alleviation. South Africa has also made substantial progress in reaching Target 10 of Goal 7, which relates to access to safe drinking water. Since 1994, South Africa has started to address the basic services backlog. Between 1996 and 2011, households with access to water increased from 76.6 per cent to 90.8 per cent, while those with access to improved sanitation facilities increased from 49.3 per cent in 1996 to 66.5 per cent in 2011 (The Presidency 2013), making this target likely to be achieved for South Africa.

Finally, MDG8 deals with global partnerships toward development. South Africa supports various initiatives within Africa, and the rest of the developing community, including for instance becoming a member of the World Trade Organisation (WTO) or championing the New Partnership for Africa's Development (NEPAD). Not all the MDGs will be included in our modelling. The focus will be on MDGs 2, 4, 5, 6, (representing education and health goals). The purpose of the study is not to impose any hierarchy on the MDGs, but to try to simulate an improvement in the general situation within the time constraints.

The Model Used

In order to evaluate if South Africa can achieve selected MDGs, a dynamic CGE model based on the CGE developed by [START_REF] Chitiga | The impact of the international crisis in South Africa[END_REF] is used. To this, a specific module for studying the MDGs is added, based on [START_REF] Lofgren | MAMS: An Economywide Model for Analysis of MDG Country Strategies: Technical Documentation[END_REF] specifications. Following [START_REF] Lofgren | MAMS: An Economywide Model for Analysis of MDG Country Strategies: Technical Documentation[END_REF], it is assumed that each year, a student can graduate (grd), repeat (rep) or drop out (drop).When a student graduates (grd), he/she can be graduated within the cycle (cont_cyc) or the last year of the cycle (grd_cyc). Finally, when a student finishes a cycle, he/she can go on to the next cycle (grd_cont) or decide to leave the education system and enter the labour market (grd_quit). The intake rate (g1entry), students' behaviour to graduate (grd), and to graduate and go on to the next cycle (grd_cont) are computed using a logistic function. The rationale behind using such a function is to show that if the original value is quite low, with a small investment, it is easy to improve the value. Conversely, if the original value is quite high, it will be quite difficult to improve it and reach the limit value.

For each cycle, student behaviours' are influenced by the quality of education, the wage rate differential and the student's health. It is indeed easy to understand that if the government decides to hire more teachers/professors, ceteris paribus, it will reduce the teacher per student ratio, and therefore increase the quality of education. In this case, this will have a positive influence on the student who will then be keen to go on studying. After each year, students who graduate from a cycle will enter the corresponding labour market. For instance, we assume that students that do not complete their primary level, or complete and enter the labour force, will be considered as unskilled workers on the labour market. Students completing the secondary education level will enter the labour market as semi-skilled workers. Those who do not graduate from the secondary education level will enter the labour market as unskilled workers. Finally, students who finish their tertiary education level will enter the labour market as skilled workers. Those who do not graduate the tertiary level will enter the labour market as semi-skilled workers. This way, the retroactions and interdependencies between the education sectors and the labour market can clearly be seen. To compute the value of the education MDG (MDG2), the intake rate and the graduation rate for the length of the primary school are multiplied. To take into account the other MDG (MDG 4, 5 and 6), we also use a logistic function. In this case, the arguments of the function are health services and water services supplied by government and per capita consumption. The details and list of the full model equations and description are available from the authors upon request to the interested reader.

Data Description

The data is based on the Social Accounting Matrix (SAM) of 2005 developed by Quantec. The SAM contains 56 activities and 56 commodities (after adjustment for education), two broad factors (labour and capital), four institutional sector accounts (households, enterprises, government and the rest of the world), and two saving and investment accounts. In the original Quantec SAM, the education sector includes the three levels (primary, secondary and tertiary). For purposes of this study, we split the education sector between these three components. To proceed, we use the government spending shares from the Reserve Bank for 2005.

In addition to the SAM, there is need to assign values for the number of students and for their behaviour at the base year. Indeed, the number of students and the different shares for the base year are observed values. For the following years, the model will compute them as they will be influenced by the different policies. The numbers of students per cycle (primary, secondary and tertiary) are taken from the Department of Education ( 2009). According to the South African Department of Education's descriptions, primary education goes from Grade 1 to Grade 7, secondary education from Grade 8 to Grade 12, while tertiary (higher) education includes universities, technikons and further education technical (FET) colleges.

The intake rate is computed from the Department of Education (2009). For the primary level, the share of students that graduate (grd) and repeat (rep) are taken from the Department of Education (2009). Assuming that each year, a student can either graduate, repeat or drop out, the sum of these three shares is equal to one. Therefore, we can find the share of students that drop out by difference. Transition rate (grd_cont), which is defined as the share of students that end a cycle and get into the next cycle, from Grade 7 to Grade 8, is taken from the Department of Education figures and is quite high, at 96 per cent. As a student can either continue to the next level, or enter the labour market, the sum of these two shares adds up to one. We can thus compute by difference the share of students that enter the labour market after graduating from the primary level. For the secondary level, for graduation rates, the results of the matric (exam at the end of Grade 12) were taken. For Grade 12, the repetition rate is 0.9 per cent, and the difference constitutes the dropout rate.

To compute transition rates, the following assumption was made: the Department of Education provided the share of students that pass matric and are allowed to go onto university (17 per cent). However, to be highly skilled, students can also attend technikons and FET colleges. Therefore, this share is increased to 75 per cent because most of the students that complete secondary education continue into higher education; in the absence of another share, this is assumed to be the correct one.

For the tertiary level, as no data exists for higher education, the following assumptions were made: 50 per cent of the students graduate and very few of them repeat (5 per cent). Informal discussions with key informants indicated that the number of students repeating a whole programme (as opposed to a course) is very low at tertiary institutions, as students will just rewrite subjects they fail. For transition rate, the share of students that graduate and enter the labour market is obviously equal to 100 per cent as students cannot go further. Table 1 summarises the different shares at the base year.

Results

Given that 2015 is around the corner, we know that it is not possible for South Africa to achieve all the MDGs. In section 2 above, we pointed out that some of the MDGs were already achieved. On the other hand, for some others, it seems infeasible to reach them (especially MDG4 and MDG5). As underlined in the discussion above, these two MDGs are strongly related to the HIV situation. In other words, targeting the MDG6 (HIV) will have indirect positive impacts on MDG4 and MDG5. We explained as well above that MDG2 (the education related MDG), is also crucial (because of the links it has with other MDGs) and almost achieved. Therefore, the first scenario will focus on how much it would take to reach MDG2 (universal education) at the end of 2015. The second scenario will focus on reaching MDG6 (HIV indicator), knowing that improving it will have positive impacts on other MDG indicators. For both scenarios, the assumption is made that government borrows from domestic agents, and no fiscal policy adjustment is available to finance the policy attainment of the selected MDGs1 .

Scenario 1: Reach MDG2 in 2015

This scenario consists of reaching MDG2 (universal education) and looking at the cost in terms of primary education public spending compared to a situation without the policy. As explained earlier, improving the skills level of the population will have positive spillovers for the other MDGs, by creating more skilled people for the economy in the long run. Table 2 shows how much extra the government has to spend. Increased public spending also has an impact on the whole economy. As government hires more people (to teach, to build new schools etc.), the effect on labour demand, and therefore on unemployment rates, is positive. A general equilibrium effect occurs, which means that government carries the other sectors of the economy through backward and forward linkages. The categories that really benefit from the policy are highly and semi-skilled labour, and the effect is negligible for low-skilled workers. The impacts on households' income and consumption are quite positive (1.14 percent).

For the government, given the increase in households' direct taxes and indirect taxes, its income is increasing. However, not surprisingly, government savings decrease due to the absence of fiscal reform to compensate for the policy. Indeed, it has been assumed that no fiscal policy is set up, and therefore, government is borrowing from domestic agents. Consequently, domestic investment is affected as firms are normally the main contributors to total investment. The fall in private investment shows a typical crowding-out effect. From Figure 1, it can be discerned that GDP increases slightly. The impacts on other MDGs are also positive, due to the increase in households' consumption.

Scenario 2: Reach MDG6 in 2015

This scenario simulates reaching MDG6 in 2015. According to the report on South Africa's MDGs, this objective is attainable (UNDP, 2007:75). In order to reach the target, government increases its consumption of health services. In other words, it builds extra hospitals, improves the transport system to enable people to reach their health centres, which allows more people access to free treatments and so on. As Table 3 shows, by 2015 government' consumption for health services would increase by 17.4 per cent. Targeting MDG6 has positive knock-on effects for other MDGs, especially MDG4 and MDG5. The general improvement of health also affects the education indicator (MDG2), as children who are not sick can go to school and follow a normal school life. The implementation of the policy has positive effects on the entire economy. Indeed, government needs to hire new doctors and nurses, as well as other people in order to build new care centre, and this has a positive impact on the level of employment. Unemployment decreases for each type of worker, especially for skilled and highly skilled workers. The impact on households is also positive, as their income increases by 0.63 per cent in 2015, and their dissaving decreases.

The level of direct taxes collected also increases, which leads to government's income increasing by 0.34 per cent in 2015. However, government's savings decrease by just over 14 per cent in 2015. In order to finance its policy, government borrows from the domestic market. This increase in public borrowing, mainly from the domestic firms, has an impact on total investment (IT). The same phenomenon occurs as in the previous scenario, with public investment (IT_PUB) having a crowding-out effect (Table 4).

Conclusion

This paper is one of the first applications in the region that looks at ways in which government might reach the Millennium Development Goals by increasing spending. For South Africa, reaching all the MDGs seems impossible, especially MDG4 and MDG5 (child and mother-related health goals), as the actual values are too far away from the target values. The results were quite promising for universal primary education (MDG2) and combating HIV-AIDS (MDG6), but in both simulations government has to borrow (from the domestic firms) to reach the MDG target. This is not sustainable in the long run, and increasing indirect taxes in order to reach the MDG target could harm households' spending, eventually reducing any benefits. This does not mean that little progress can be made to improve public health resources. Instead, the findings suggest that the post-2015 health agenda must be characterised by continuation of MDGs 4,5 and 6 with more effort at reducing child and maternal mortality and the fight against HIV and AIDS, TB and malaria should not stop in 2015 but intensify. In doing so, however, government should carefully weigh up the impact of increasing spending against the risk associated with increasing taxation rates, spending levels and deficit finance.

Figure I :

 I Figure I: Impact on GDP (at basic prices)

Table I : Shares of student's behaviours

 I

			2005
	g1entry	primary	0.515
	grd	primary	0.930
	grd	secondary 0.683
	grd	tertiary	0.500
	grdcont	primary	0.960
	grdcont	secondary 0.750
	grdcont	tertiary	0.000
	grdquit	primary	0.040
	grdquit	secondary 0.250
	grdquit	tertiary	1.000
	rep	primary	0.003
	rep	secondary 0.009
	rep	tertiary	0.050
	dropout	primary	0.007
	dropout	primary	0.041
	dropout	secondary 0.308
	dropout	tertiary	0.450
	Source: Various publications and own assumptions

Table II : Impact on government spending (in per cent compared to BAU)

 II

	Years	Government
		consumption in
		'primary'
	2011	1.24
	2012	3.38
	2013	6.46
	2014	10.84
	2015	23.57
	Source: Own computations based on the model

Table III Impact on government's consumption on health services (in per cent compared to BAU)

	Year	Government's consumption
		in health services
	2011	3.27
	2012	6.37
	2013	10.09
	2014	13.66
	2015	17.40
	Source: Own computations based on the model

Table IV : Impact on investment: (in per cent compared to BAU)

 IV

		IT	IT_PRI	IT_PUB
	2015	-1.98	-2.38	0.07
	Source: Own computations based on the model

For extra policy simulations, the interested reader can refer to[START_REF] Mabugu | Realising The Millenium Development Goals Through Interregional Fiscal Transfers In South Africa[END_REF]


John Cockburn

Martin Henseler

Hélène Maisonnave

Luca Tiberti
email: luca.tiberti@ecn.ulaval.ca

Vulnerability and policy responses in the face of natural resource discoveries and climate change: introduction

Keywords: Developing countries, economic growth, natural resources, resource curse

This special issue contributes to the natural resource economics literature by shining a light on the specific challenges and opportunities faced by developing countries that have recently become dependent on natural resources or are particularly exposed to climate change. It is composed of five studies on countries from all regions of the developing world, involving a variety of natural resources and policy issues. Four of the five studies illustrate how computable general equilibrium models are particularly well-suited, despite their relatively limited past use, to the analysis of natural resources. All five studies are led by researchers based in these countries, providing unique insights into the specific local context. The studies underscore the extreme vulnerability that the introduction of significant natural resource revenues and climate change can create in developing countries. They also show how the choice of appropriate policies to avoid the resource curse varies according to country-specific economic conditions.

Economic dependency on natural resources

Economic growth and poverty reduction are crucial policy objectives, particularly in developing countries. When developing countries discover natural resource endowments, their exploitation provides a unique opportunity to pursue these objectives. However, such discoveries can also pose significant risks. Careful management of natural resources and appropriate accompanying policies are essential to avoid potential negative impacts on economic development (i.e., the resource curse) and to ensure that the resulting growth is as inclusive as possible (OECD, 2008).

The contribution of the rents from natural resources to GDP varies substantially across the various regions of the world (see top half of table 1). In general, such rents are much more important for low income countries, among which the Middle East & North Africa and Sub-Saharan Africa are the most natural resource-dependent regions. Source: World Bank (2017a).

Note: ND -no data.

In the context of this special issue, we focus on a group of countries where mineral resources have only recently emerged as an important sector of the economy: Burkina Faso, Chad, Mongolia and Niger. In Burkina Faso, Chad and Mongolia, natural resource rent shares in GDP increased multifold between 2000 and 2010 (see bottom half of table 1), although falling world commodity prices reduced these shares in Chad (oil) and Mongolia (coal and copper) by 2015 (see figure 1). The progression in Niger (uranium and oil), and continued growth in Burkina Faso (gold), has occurred since 2010, despite falling world prices for oil and gold. To provide a broader overview of the natural resource management issue, we also include Guatemala, which is a country that relies heavily on non-mining natural resources -water and land -agriculture.

Table 1 also illustrates the extreme volatility of natural resource rents. In all world regions, we observe dramatic peaks in rent shares in 1980 and 2005, corresponding to soaring world commodity prices, followed in each case by precipitous declines. Among our case study countries, natural resource rents fell by roughly half between 2010 and 2015 in Chad and Mongolia. This volatility creates uncertainty and vulnerability.

The debates on natural resources in developing economies

Faced with the growing importance of natural resources in the economy for developing countries and the paradox that well-endowed countries often perform less well than non-endowed countries, economists have pursued three channels of reflection [START_REF] Barbier | The role of natural resources in economic development[END_REF]: (i) resource depletion and sustainable resource management, (ii) environmental degradation and the environmental Kuznets curve hypothesis, and (iii) the resource curse.

(i) Resource depletion and sustainable resource management

The problems of depletion apply to the exploitation of both renewable and nonrenewable natural resources. The overexploitation of renewable resource stocks (e.g., forestry, fish stocks, water, soil) can lead to irreversible stock depletion. The depletion of non-renewable natural resources (e.g., fossil fuels, minerals) is unavoidable, although technological progress and discoveries can provide access to new resource stocks to prolong the period of exploitation. This said, increased efficiency in exploitation technology may also accelerate wasting (OECD, 2008).

Resource depletion may affect welfare directly in the short term or may only manifest for future generations [START_REF] Barbier | The challenges for environment and development economics[END_REF]. Sustainable resource management aims to avoid or limit the negative impacts of depletion. It requires measurement of the rate of depreciation of natural stocks and consideration of the resource-growth nexus in its full complexity [START_REF] Santopietro | Alternative methods for estimating resource rent and depletion cost: the case of Argentina's YPF[END_REF][START_REF] Rammel | Managing complex adaptive systems -a co-evolutionary perspective on natural resource management[END_REF][START_REF] Dauvin | The paradox of plenty: a meta-analysis[END_REF]. This may involve the enforcement of sustainable extraction rates for renewable resources to allow for the regeneration of the stocks (e.g., fish harvesting). For nonrenewable resources, sustainable resource management includes the re-investment of natural resource rents into other sectors, which can compensate for the loss of natural capital by depletion (Hartwick-Solow rule) [START_REF] Lange | Sustainable development in mineral economies: the example of Botswana[END_REF].

(ii) Environmental degradation and the environmental Kuznets curve hypothesis

The exploitation of natural resources can cause environmental degradation directly through the extraction process of non-renewable resources (e.g., environmental pollution from mining) and through the exploitation of renewable resources (e.g., ecological damages from deforestation), and indirectly (e.g., CO 2 emissions from the use of fossil fuels). The negative impacts of environmental degradation (e.g., on health and income) usually affect the poor disproportionately to the rich and sometimes even result in displacement or migration (Laczko and Aghazarm, 2009).

The environment Kuznets curve (EKC) hypothesis explains how the environmental degradation depends on the wealth of a country. It describes the relationship between environmental degradation and per capita income as an inverted U-shape [START_REF] Barbier | Introduction to the environmental Kuznets curve special issue[END_REF][START_REF] Barbier | The role of natural resources in economic development[END_REF]. Many studies find empirical evidence in favour of the EKC hypothesis for different environmental indicators: e.g., for deforestation [START_REF] Bhattarai | Governance, economic policy, and the environmental Kuznets curve for natural tropical forests[END_REF], electricity consumption (Burke, 2012), emissions (Cole, 2003;[START_REF] He | China's industrial SO2 emissions and its economic determinants: EKC's reduced vs. Structural model and the role of international trade[END_REF][START_REF] Lipford | Environmental Kuznets curves, carbon emissions, and public choice[END_REF] and multiple environmental indicators (Cole et al., 1997).

(iii) The resource curse

The debate surrounding the effects of natural resource exploitation on economic growth (e.g., the resource curse) intersects with the debates on resource depletion (see e.g., [START_REF] Vincent | Resource depletion and economic sustainability in Malaysia[END_REF][START_REF] Neumayer | Does high indebtedness increase natural resource exploitation?[END_REF] and environmental degradation (see e.g., Burke, 2012;[START_REF] Abou-Ali | Integrated paradigm for sustainable development: a panel data study[END_REF].

The resource curse describes the paradox that economic growth in many resourcerich developing countries lags behind resource-poor developing countries. Many resource-rich developing countries structure their development around their exploitation. However, they often exploit their resources inefficiently and fail to reinvest natural resource rents in other productive investments [START_REF] Barbier | The role of natural resources in economic development[END_REF]. Instead of the expected benefits of windfall revenues from natural resources, the resource curse can provoke negative impacts: reduced economic growth, increased poverty and/or inequality, conflicts and political instability [START_REF] Siakwah | Are natural resource windfalls a blessing or a curse in democratic settings? Globalised assemblages and the problematic impacts of oil on Ghana's development[END_REF].

Many studies explore the various causes of the resource curse. The following presentation provides a basic overview drawing on the most recent literature [START_REF] Badeeb | The evolution of the natural resource curse thesis: a critical literature survey[END_REF][START_REF] Dauvin | The paradox of plenty: a meta-analysis[END_REF][START_REF] Hailu | The Extractives Dependence Index (EDI)[END_REF][START_REF] Siakwah | Are natural resource windfalls a blessing or a curse in democratic settings? Globalised assemblages and the problematic impacts of oil on Ghana's development[END_REF].

(a) The 'Dutch Disease' describes the macro-economic mechanism whereby increased natural resource exports lead to a real currency appreciation that penalizes other tradable sectors. Separate 'spending' and 'pulling' effects are distinguished. The spending of increased natural resource revenues increases wages and non-tradable prices, which cuts profits in other tradable sectors faced with fixed world prices. At the same time, resources are pulled from these other tradable sectors to fuel the natural resource sector. Both effects can result in the contraction of the non-resource tradable sectors and thus hamper long-term economic growth [START_REF] Badeeb | The evolution of the natural resource curse thesis: a critical literature survey[END_REF][START_REF] Dauvin | The paradox of plenty: a meta-analysis[END_REF].

(b) Vulnerability. On the one hand, volatility in global commodity prices causes pro-cyclical fluctuations in government revenues and export earnings and also reduces investment, especially in countries with poor financial development. Vulnerability can also stem from variability in the availability of renewable resources (e.g., fish stocks) or production factors (e.g., water and sun for agriculture).

(c) Economic mismanagement applies if, in the face of windfall revenues, the government fails to apply appropriate policy measures to counter the resource curse. This includes inappropriate or insufficient investment of resource rents in physical or human capital (e.g., in infrastructure, education) or inappropriate reform of fiscal policies (e.g., increasing tax collection, creating resource-funded fiscal cushions) [START_REF] Badeeb | The evolution of the natural resource curse thesis: a critical literature survey[END_REF]. A recent body of literature focuses on different spending strategies to increase growth and improve welfare through the Bird in Hand theory or the Permanent Income Hypothesis (see e.g., Collier et al., 1997;[START_REF] Van Der Ploeg | Natural resources: curse or blessing?[END_REF][START_REF] Van Der Ploeg | Harnessing windfall revenues: optimal policies for resource-rich developing economies[END_REF][START_REF] Arezki | Commodity Price Volatility and Inclusive Growth in Low-Income Countries[END_REF][START_REF] Go | Natural resource revenue, spending strategies and economic growth in Niger[END_REF].

(d) Rent seeking refers to efforts to appropriate natural resource rents by elites who have the capacity to influence policy decisions. The resulting inequalities and poverty can be avoided by redistributive policies that increase the benefits for the poor [START_REF] Bourguignon | Commodity price volatility, poverty, and growth inclusiveness in sub-Saharan African countries[END_REF][START_REF] Badeeb | The evolution of the natural resource curse thesis: a critical literature survey[END_REF]. Pro-poor investments can favour economic growth by increasing the purchasing power of the economy and building human capital (e.g., education, health), which increases labour supply and productivity and can reduce poverty in the long term (see [START_REF] Robichaud | Impact of increased public education spending on growth and poverty in Uganda. An integrated micro-macro approach[END_REF][START_REF] Alter | Public investment in a developing country facing natural resource depletion[END_REF].

(e) Low institutional quality can lead to reduced growth and increased poverty and inequality. Ideally, strong institutions ensure policies to foster economic growth and share benefits with the poor. However, windfall natural resource revenues can undermine the quality of institutions and result in widespread corruption [START_REF] Badeeb | The evolution of the natural resource curse thesis: a critical literature survey[END_REF].

The academic literature addresses the resource curse and economic growth in many empirical studies (e.g., [START_REF] Gylfason | Natural resources, education, and economic development[END_REF][START_REF] Sachs | The curse of natural resources[END_REF] and in meta analyses and literature reviews (e.g., [START_REF] Havranek | Natural resources and economic growth: a meta-analysis[END_REF][START_REF] Badeeb | The evolution of the natural resource curse thesis: a critical literature survey[END_REF][START_REF] Dauvin | The paradox of plenty: a meta-analysis[END_REF][START_REF] Papyrakis | The resource curse -what have we learned from two decades of intensive research? Introduction to the special issue[END_REF]. This literature mainly focuses on countries that began the exploitation of natural resources decades ago. Few studies explore the adaptation of countries to sudden increases in natural resource revenues.

This special issue presents studies on natural resources and economic development for five developing countries -Burkina Faso, Chad, Guatemala, Mongolia and Nigerthat have recently discovered natural resources or started to face problems in their management. It focuses primarily on the third debate above, i.e., the design of appropriate policies to avoid the resource curse.

The studies in the special issue

This special issue presents the findings on the relationship between natural resources and economic development for five developing countries. All five studies included here have been led and conducted by teams of researchers from and living in these countries, thus providing unique insights into the issues involved and the nuanced and complex implications, as well as a privileged access to information and knowledge of their local context.

Each case study included in this issue presents a different natural resource, i.e., water in the case of Guatemala, gold for Burkina Faso, uranium and oil in Niger, coal and copper in Mongolia, and oil in the case of Chad. The macro-and micro-economic effects vary according to the type of natural resource and specific characteristics of each country, as they involve, for example, different factor intensities (e.g., agricultural activities are more intensive in unskilled labour than most mining activities) and different degrees of foreign control over the resources in question.

All five studies simulate one or more policy scenarios concerning the management of natural resources. Four of the five studies adopt computable general equilibrium (CGE) models, while the fifth uses an ex-post micro-analytical approach. One of the key contributions of this special issue is to illustrate how CGE models, which are under-represented in the natural resource literature, can constitute an excellent tool to analyse complex macro-micro issues related to natural resource management. The authors design scenarios closely based on local, policy-relevant forecasts, legislation and recommendations.

While the papers in this special issue provide a large number of country-specific insights, outlined in the individual papers, two common threads emerge. First, the Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1355770X18000347 Downloaded from https://www.cambridge.org/core. Bibliotheque de l'Universite Laval, on 30 Jul 2018 at 14:09:10, subject to the Cambridge sudden emergence of natural resource rents and climatic change both create particular issues of overdependence and vulnerability in developing countries. Second, the choice of appropriate policies to avoid the resource curse depends crucially on the specific characteristics of the natural resources and country in question, in ways that allow local researchers to provide particularly robust and unique insights.

Vulnerability to global price volatility and climatic change

In table 1, we observed the significant variations in natural resource rents in all regions of the world due to global commodity price volatility, with peaks in 1980 and 2005 followed by significant declines. If we focus on the key natural resources for our five case studies, we can observe the substantial volatility of global prices since 2000 (see figure 1). [START_REF] Baatarzorig | Effects of ups and downs of the Mongolian mining sector[END_REF] study the impacts of global price volatility in Mongolia, which has recently become highly dependent on the mining of copper and coal. Under the assumption that the current copper mining projects (e.g., Oyu Tolgoi project) continue their production until 2020, they simulate a 20 per cent decline in copper prices. Since the economy is largely dependent upon the mining sector, the impacts of the shocks are jarring, with GDP declining by 1.2 per cent and overall employment by 5 per cent. The authors recommend the creation of financial stabilization funds to reduce the country's vulnerability to global price changes.

In Burkina Faso, gold has recently replaced cotton as the country's main export, exposing the country to impacts from volatility in global gold prices. The Burkinabe has responded by reforming the mining tax code. Sisso and Beaumais (2018) simulate a 15 per cent decrease in the price of gold and find that this reduces real GDP by 0.74 per cent, employment by 3 per cent and public revenues by 6 per cent. They show that the landlocked nature of the economy and the poorly-developed financial systems make Burkina Faso particularly vulnerable to shocks in world gold prices.

In the case of agricultural goods, climatic change is an additional source of vulnerability for resource-dependent developing countries. In Guatemala, [START_REF] Vargas | Climate risk and food availability in Guatemala[END_REF] simulate climate change scenarios according to forecasts by CEPAL (2013). Guatemala is characterized by low food security and high vulnerability to the impacts of climate change on the availability of water for agriculture, a key sector of the Guatemalan economy. The forecasted drop in rain water supply negatively affects the productivity of the agricultural sector and, as a consequence, significantly impacts the whole economy, resulting in a decrease in food exports, household income and food security. The study shows that, to ensure economic growth, welfare and food security in the face of volatility in water supply, the instauration of a legal framework to manage water supply is critically urgent. The authors also establish that regional redistribution policies for water can increase welfare and food security, while reducing poverty and inequality. [START_REF] Sisso | Gold price volatility, tax receipts and employment: can Burkina Faso's adaptation strategy avoid the resource curse?[END_REF] assess the impacts of the 2014 mining code in Burkina Faso, which increases the taxation of firms in the gold mining sectors. The authors find that the policy slightly increases government income (0.3 per cent) and spending by 0.42 per cent. However, as the gold sector is only weakly linked to other sectors, the effects on the rest of the economy are negligible. The authors conclude that a more effective policy would be to encourage collaboration between mining companies and domestic industries as part Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1355770X18000347 Downloaded from https://www.cambridge.org/core. Bibliotheque de l'Universite Laval, on 30 Jul 2018 at 14:09:10, subject to the Cambridge of mining contracts. This policy could promote development of domestic industries, job creation, and an increase in tax revenue from mining.

Policy to avoid the resource curse

Niger forecasts an increase in its oil exports through the exploitation of new oil reserves and the development of new transport and refinery capacities. Niger will also start exploiting a new uranium deposit in 2017, and should become the second largest producer in the world. To avoid the resource curse -notably for Niger's important agricultural sector -and to increase economic growth, the government plans to re-invest natural resource rents to address its underdeveloped transport infrastructure. [START_REF] Sangare | Mining and petroleum boom and public spending policies in Niger: a dynamic computable general equilibrium analysis[END_REF] find that this policy would increase long-run production in services (0.05 per cent), agriculture (0.03 per cent) and the whole economy (real GDP increases by 0.04 per cent). The finding is in line with recent literature showing that infrastructure investments may help avoid the resource curse.

In Chad, rent seeking behaviour by elites and weak institutional quality have hindered rent redistribution policies, although they remain objectives of its Poverty Reduction Strategy and National Development Plan. [START_REF] Gadom | The impact of oil revenues on wellbeing in Chad[END_REF] use an ex-post microeconomic impact evaluation analysis to assess the effect of oil revenues on well-being. While revenues from oil exploitation are found to substantially improve multidimensional well-being, an inappropriate and discretionary use of such revenues is likely to further exacerbate existent inequalities in Chad. A few departments, including the capital city and its neighbours, receive a significantly larger share of oil revenues relative to their needs, which translates into a substantially bigger improvement in their wellbeing. In order to avoid the resource curse at the national level, the authors recommend an inclusive governance of natural resources to redistribute oil rents according to local development, socio-demographic and primary infrastructure needs.

Mongolia expects a moderate boom in its coal mining sector in the face of increased demand from China. Historically Mongolia followed a pro-cyclical fiscal policy, which is the expected future policy. Yet this risks exacerbating the effects of the boom and Dutch disease. While [START_REF] Baatarzorig | Effects of ups and downs of the Mongolian mining sector[END_REF] conclude that Mongolia is less vulnerable to these effects than most other developing countries due to the near absence of other tradable sectors, they find that a countercyclical policy is more appropriate.

Concluding remarks

This special issue complements the large body of existing literature on the relationship between natural resources, economic growth and social welfare in developing countries. The studies focus on an underanalysed aspect of this literature: countries where natural resources have only recently emerged as key sources of revenues and the specific challenges and opportunities this represent. A variety of natural resources, countries (from all regions of the developing world) and policy issues are analysed using both macro and micro methods of analysis.

The studies show how the sudden emergence of natural resource revenues in a developing country can quickly create problems of dependence and vulnerability to volatility in global prices and climate change. Policy interventions to counteract such problems range from the creation of financial stabilization funds (in Mongolia, copper and coal) to the instauration of a legal framework to manage water supply and the establishment of regional redistribution policies for water (in Guatemala, water). They also outline appropriate policies to manage these new-found natural resources to avoid the resource curse, underscoring the importance of adapting to the specific characteristics of the natural resources and country in question. In such a case, the policy interventions

Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1355770X18000347 Downloaded from https://www.cambridge.org/core. Bibliotheque de l'Universite Laval, on 30 Jul 2018 at 14:09:10, subject to the Cambridge proposed in this volume include countercyclical policies (in Mongolia, copper and coal), redistribution of oil rents according to various local development criteria (in Chad, oil), and investment of natural resource rents into transport infrastructure and indication of a collaboration between mining companies and domestic industries as part of mining contracts (in Burkina Faso, gold).

The findings of these studies can practically support the local political decisionmaking processes and the design and evaluation of policies.

This special issue contributes to the literature in a number of ways. It shines a light on the specific issue of the sudden emergence of natural resource rents in a developing country. Four of the five studies adopt a CGE approach and illustrate how this methodology, relatively rare in the natural resource economics literature, is particularly appropriate to the analysis of the complex and economy-wide issues involved. All five studies were led by local researchers, who have a deep and unique perspective on the context of their specific countries.

Figure 1 .

 1 Figure 1. Variation of (real) prices of selected natural resources from 2000 to 2015 (base 100 in the year 2010) Notes: (a) Average price for crude oil. Source: World Bank (2017b). (b) Price for coal from Australia. Source: World Bank (2017b). (c) Price for copper price. Source: World Bank (2017b). (d) Price for gold. Source: World Bank (2017b). (e) Price for natural uranium. Source: ESA (2017).

Table 1 .

 1 Development of economic dependency on natural resource in the economy of world regions and selected developing countries

			Percentage share of natural resource rents in GDP
		1970	1980	1990	2000	2005	2010	2015
	World regions
	High income countries	0.7	4.5	1.3	1.3	1.8	1.9	1.1
	East Asia & Pacific	1.8	19.1	8.8	3.5	5.6	6.2	1.5
	Europe & Central Asia	0.7	1.4	9.6	9.9	11.0	9.3	6.2
	Latin America & Caribbean	1.1	8.2	4.9	3.7	6.4	5.2	2.7
	Middle East & North Africa	0.4	25.3	14.4	16.7	27.4	20.6	9.5
	Sub-Saharan Africa	4.7	19.1	14.8	13.3	16.8	14.8	8.0
	Case studies
	Burkina Faso -Gold	6.8	8.3	6.8	6.0	7.2	14.9	21.0
	Chad -Oil	4.0	10.1	7.5	10.6	38.6	24.5	13.1
	Mongolia -Coal, Copper	ND	ND	8.7	7.9	21.6	38.6	16.5
	Niger -Oil, Uranium	2.2	3.4	5.4	9.1	9.6	10.1	14.8
	Guatemala -Water	1.2	2.1	1.8	1.5	1.5	2.6	2.3

Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1355770X18000347 Downloaded from https://www.cambridge.org/core. Bibliotheque de l'Universite Laval, on 30 Jul 2018 at 14:09:10, subject to the Cambridge

Acknowledgements. This research work was carried out with financial and scientific support from the Partnership for Economic Policy (PEP) (www.pep-net.org) with funding from the Department for International Development (DFID) of the United Kingdom (or UK Aid), and the Government of Canada through the International Development Research Center (IDRC).

Fund, pp. 187-224. Burke PJ (2012) Climbing the electricity ladder generates carbon Kuznets curve downturns. Australian Journal of Agricultural and Resource Economics 56, 260-279. CEPAL (2013) Impactos Potenciales del Cambio Climático sobre los Granos Básicos en Centroamérica. Sede Subregional de la CEPAL en México, Comisión Económica para América Latina y El Caribe (CEPAL). Available at http://archivo.cepal.org/pdfs/Mexico/2013/M20130042.pdf (in Spanish). Cole MA (2003) Development, trade, and the environment: how robust is the environmental Kuznets curve? Environment and Development Economics 8, 557-580. Cole MA, Rayner AJ and Bates JM (1997) The environmental Kuznets curve: an empirical analysis. Environment and Development Economics 2, 401-416.


domain: spi phys

text:
Nicolas Renard

Sébastien Deck

On the convection velocity of wall-bounded turbulence resolved by ZDES mode III at Re θ = 13 000

WMLES simulations of a flat-plate zero-pressure-gradient boundary layer are done with the Zonal Detached Eddy Simulation Mode III technique over a wide range of Reynolds numbers 3 150 ≤ Re θ ≤ 14 000. A WMLES field is compared with the WRLES interpolated onto the WMLES mesh. Two interface heights are considered, y interface = 0.1δ and y + interface = 3.9 √ Re τ . The prediction and resolved fraction of mean skin friction is discussed, as well as remaining issues, especially in the logarithmic layer. An excess of high-wavelength streamwise velocity fluctuations is observed below the RANS/LES interface with y + interface = 3.9 √ Re τ , and studied by a spectral convection velocity analysis, leading to the suggestion that it may be a footprint of coherent structures located further away from the wall.

1 Short discussion of the need and options for Wall-Modelled Large Eddy Simulation in applied aerodynamics

In applied aerodynamics, the increasing demand for the prediction of phenomena such as mild flow separations, strongly out of equilibrium boundary layers, aeroacoustics or unsteady loading may require a more detailed and universal description than the mean values provided by Reynolds Averaged Navier-Stokes models, motivating turbulence-resolving approaches of wall-bounded flows. However, in high Reynolds number attached turbulent boundary layers in most aerospace applications (Re τ ≈ 10 4 -10 5 ), the numerical cost of Direct Numerical Simulation, and even of Wall-Resolved Large Eddy Simulation, is prohibitive because of the lack of scale separation in the near-wall region. Introducing wall models and resolving Nicolas Renard Onera The French Aerospace Lab, F-92190 Meudon, France, e-mail: nicolas.renard@onera.fr

Sébastien Deck

Onera The French Aerospace Lab, F-92190 Meudon, France, e-mail: sebastien.deck@onera.fr the outer layer dynamics, the number of grid points for Wall-Modelled Large Eddy Simulation is approximately proportional to the square root of the number of points for DNS (see [START_REF] Deck | Zonal Detached Eddy Simulation (ZDES) of a spatially developing flat plate turbulent boundary layer over the Reynolds number range 3 150 ≤ Re θ ≤ 14 000[END_REF]), making WMLES affordable in applied aerodynamics at high Reynolds numbers.

Examples of wall models ( [START_REF] Piomelli | Wall-layer models for large-eddy simulations[END_REF]) are a dynamic wall boundary condition, a nearwall mesh superimposed to the LES mesh ( [START_REF] Park | An improved dynamic non-equilibrium wall-model for large eddy simulation[END_REF]), or a lower-resolution turbulence model near the wall. In the latter option, a RANS near-wall description may be coupled to an outer LES, which naturally lies within the hybrid RANS/LES framework where LES is performed in the regions of interest, e.g. massive separations, free shear layers or the outer regions of attached boundary layers where resolving turbulence is needed, while a RANS treatment of the rest of the flow, especially some thin boundary layers, reduces the overall numerical cost ( [START_REF] Sagaut | Multiscale and multiresolution approaches in turbulence -LES, DES and Hybrid RANS/LES Methods: Applications and Guidelines[END_REF]). The near-wall RANS may for instance be a constraint for LES ( [START_REF] Chen | Reynolds-stress-constrained large-eddy simulation of wall-bounded turbulent flows[END_REF]) or blended with the outer LES ( [START_REF] Gieseking | Compressible-Flow Simulations Using a New Large-Eddy Simulation/Reynolds-Averaged NavierStokes Model[END_REF]).

In the case of Detached Eddy Simulation ( [START_REF] Spalart | Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach[END_REF], [START_REF] Spalart | Detached-Eddy Simulation[END_REF]), the same turbulence model is simply used as the RANS model near the wall and as the subgrid scale model for the outer LES by switching the characteristic length at the RANS/LES interface, but the first attempts resulted in a log-layer mismatch and significant underestimation of mean skin friction ( [START_REF] Nikitin | An approach to wall modeling in large-eddy simulations[END_REF]). Active solutions such as stochastic forcing ( [START_REF] Keating | A dynamic stochastic forcing method as a wall-layer model for large-eddy simulation[END_REF]) raise questions as to their calibration, universality, acoustic signature and numerical robustness. Alternatively, the passive interface treatment may be improved by ad hoc functions and length scale definitions, such as in IDDES ( [START_REF] Shur | A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities[END_REF]). However, this mostly empirical formulation still deviates from the logarithmic law and highly depends on the mesh resolution [START_REF] Shen | Development of a new LES/RANS formulation[END_REF]. Instead, the simple initial DES formulation may be retained for WMLES if the RANS/LES interface height is properly defined by the user to minimise the reported difficulties. This zonal WMLES strategy is adopted for Mode III of Zonal Detached Eddy Simulation [START_REF] Deck | Recent improvements in the Zonal Detached Eddy Simulation (ZDES) formulation[END_REF] described in the next section.

A WMLES strategy: Mode III of ZDES

In ZDES (Zonal Detached Eddy Simulation [START_REF] Deck | Recent improvements in the Zonal Detached Eddy Simulation (ZDES) formulation[END_REF]) the user defines the zones of interest for LES. This technique has been extensively validated since 2003 in both academic and industrial problems ranging from the flat plate to a full airliner at flight Reynolds number [START_REF] Deck | High-fidelity simulations of unsteady civil aircraft aerodynamics: stakes and perspectives. Application of Zonal Detached Eddy Simulation (ZDES)[END_REF]. Three modes may be assigned to each flow region depending on its nature and used simultaneously as demonstrated in [START_REF] Deck | Numerical investigation of the flow dynamics past a three-element aerofoil[END_REF]. Mode III results from the demonstration of the WMLES capacity of ZDES starting in 2007 ( [START_REF] Deck | On the use of stimulated detached eddy simulation (SDES) for spatially developing boundary layers[END_REF], [START_REF] Deck | Zonal Detached Eddy Simulation of a spatially developing flat plate turbulent boundary layer[END_REF]) and is also suitable for WRLES ( [START_REF] Deck | Zonal Detached Eddy Simulation of a spatially developing flat plate turbulent boundary layer[END_REF], [START_REF] Deck | Large scale contribution to mean wall shear stress in high Reynolds number flat plate boundary layers up to Re θ = 13 650[END_REF]). For WMLES, the RANS/LES interface height should not depend on the mesh resolution ( [START_REF] Deck | Zonal Detached Eddy Simulation of a spatially developing flat plate turbulent boundary layer[END_REF]) and scale in outer units (i.e. be at a constant y/δ [START_REF] Deck | Zonal Detached Eddy Simulation (ZDES) of a spatially developing flat plate turbulent boundary layer over the Reynolds number range 3 150 ≤ Re θ ≤ 14 000[END_REF] or at the geometric centre of the logarithmic layer [START_REF] Renard | On the interface positioning in a Zonal Detached Eddy Simulation (ZDES) of a spatially developing flat plate turbulent boundary layer[END_REF], [START_REF] Renard | Improvements in Zonal Detached Eddy Simulation for Wall Modeled Large Eddy Simulation[END_REF]). The interface may typically be positioned from a pre-processing of the RANS flow field used as the initial condition for the ZDES simulation. ZDES mode III has been used on three-dimensional geometries representative of industrial problems (e.g. curved duct for dynamic distortion predictions [START_REF] Laraufie | Zonal detached eddy simulation (ZDES) study of a 3D curved duct[END_REF], high-lift three-element airfoil [START_REF] Deck | Numerical investigation of the flow dynamics past a three-element aerofoil[END_REF]). Because high-Reynolds-number attached boundary layers are ubiquitous in aerospace applications, the rest of the present study focuses on a flat plate boundary layer test case defined in the next section with as long a streamwise extent as possible.

3 Motivation, definition and visualisation of a high-Reynolds-number zero-pressure-gradient flat-plate turbulent boundary layer test case

A WMLES test case for external aerodynamics relevant to aerospace applications should at least feature spatial growth (thus excluding channel and pipe flows because of their different turbulent dynamics [START_REF] Marusic | Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues[END_REF]) and high Reynolds numbers (because there are dominant physical phenomena such as superstructures at the Re τ values typical of applications that are not visible at lower Reynolds numbers [START_REF] Smits | High-Reynolds number wall turbulence[END_REF], [START_REF] Jiménez | Cascades in wall-bounded turbulence[END_REF]). A natural choice is the zero-pressure-gradient flat-plate boundary layer, an extensively documented test case representative of attached boundary layers without strong pressure gradients. Its geometrical simplicity puts great demands on turbulence modelling, whose validation on this test case may be seen as a mandatory first step before considering more complex flows where success or failure may be more geometry-dependent.

The ZPG TBL simulated here at M ∞ = 0.21 may be compared to incompressible data and covers a wide range of Reynolds numbers, 3 150 ≤ Re θ ≤ 14 000 with the streamwise extent L x = 350δ 0 (δ 0 is the initial boundary layer thickness). Streamwise velocity spectra from a WRLES of the same test case (also performed with ZDES mode III [START_REF] Deck | Large scale contribution to mean wall shear stress in high Reynolds number flat plate boundary layers up to Re θ = 13 650[END_REF]) reproduced in fig. 1 clearly indicate the presence of superstructures (λ x ∼ 5 -6δ ) in the outer layer at Re θ = 13 000 that are not visible at Re θ = 5 200, confirming that a lower Reynolds number test case would not include superstructures despite their importance for applied aerodynamics (see e.g. their contribution to mean skin friction [START_REF] Deck | Large scale contribution to mean wall shear stress in high Reynolds number flat plate boundary layers up to Re θ = 13 650[END_REF]). τ reconstructed with a correlation-based convection velocity at Re θ = 5 200 (left) and Re θ = 13 000 (right). WRLES simulation using ZDES mode III (see [START_REF] Deck | Large scale contribution to mean wall shear stress in high Reynolds number flat plate boundary layers up to Re θ = 13 650[END_REF] and [START_REF] Renard | On the scale-dependent turbulent convection velocity in a spatially developing flat plate turbulent boundary layer at Reynolds number Re θ = 13 000[END_REF]).

For WMLES by ZDES mode III, mesh spacings ∆ x + = 200 and ∆ z + = 100 in the streamwise and spanwise directions respectively (∆ x/δ 0 = 0.212 and ∆ z/δ 0 = 0.107) are used here. The total number of grid points is N xyz = 30 • 10 6 , much less than for the aforementioned WRLES (N xyz = 800 • 10 6 with ∆ x + = 50 and ∆ z + = 12). Because ZDES is developed with industrial applications in mind, the test case is simulated with the in-house FLU3M solver with robust second-order numerical schemes suited for complex geometries. This is not optimal for the present academic test case (where higher order schemes could help) but it represents how the method will be used in real geometries. The convective fluxes are discretized by a modified AUSM+(P) scheme with a wiggle detector reducing numerical dissipation [START_REF] Mary | Large eddy simulation of flow around an airfoil near stall[END_REF] and the MUSCL state reconstruction. Time integration is second-order accurate implicit. The turbulent inflow is provided by a Synthetic Eddy Method ( [START_REF] Pamiès | Generation of synthetic turbulent inflow data for large eddy simulation of spatially evolving wall-bounded flows[END_REF], [START_REF] Laraufie | Assessment of Reynolds stresses tensor reconstruction methods for synthetic turbulent inflow conditions. Application to hybrid RANS/LES methods[END_REF]). The RANS/LES interface heights investigated here, y interface = 0.1δ and y + interface = 3.9

√ Re τ (centre of the logarithmic layer), are illustrated in fig. 3. A visual comparison of the flow resolved by ZDES near Re θ = 13 000 in WR-LES and in WMLES (y interface = 0.1δ ) is provided in fig. 2. Some features of the WRLES, especially the inclined structures visible in the numerical Schlieren suggesting hairpin packets, may be recognised in the WMLES. An insight into the finest fluctuations that the WMLES mesh can support is obtained by interpolating the WR-LES flow field onto the WMLES mesh. The comparison with the WMLES suggests that there is still room for improvement of the WMLES results, even regarding the largest-scale organisation of the flow field, as will be quantified in fig. 6.

WMLES prediction of mean skin friction by ZDES

The prediction of mean skin friction in attached boundary layers is mandatory for applied aerodynamics because of its relation to drag and to the spatial development of boundary layers. Hence a WMLES should ideally be as accurate as a RANS model with respect to this mean parameter, whose prediction by ZDES mode III is detailed in §4.1 before a few issues related to the logarithmic layer are discussed in §4.2.

Accuracy, resolution and streamwise evolution of skin friction

In the present case, with both interface heights illustrated in fig. 3, mean skin friction predicted by ZDES is within 5 % of the Coles-Fernholz correlation (fitted to experimental data [START_REF] Nagib | Approach to an asymptotic state for zero pressure gradient turbulent boundary layers[END_REF]) over the region of fully developed resolved turbulence (excluding the relaxation downstream the turbulent inflow), as shown in fig. 4. The resolved and modelled turbulent contributions are compared by plotting the resolved fraction of Reynolds shear stress u v res / u v tot in fig. 3, equal to 0 in the case of a pure RANS behaviour and equal to 1 in the case of a DNS, thus quantifying the intermediate state between RANS and LES. The simulation is pure RANS only at the wall itself, with fluctuations resolved even in the RANS region. The resolved fraction is close to 1 in the outer layer and increases from the wall to the outer edge of the boundary layer. Its monotonicity is a satisfying property since the further away from the wall, the more resolution (rather than modelling) is expected. The resolved fraction is higher with the log layer centre definition of the interface at Re θ = 13 000, which is not surprising since the interface is located much lower than the 0.1δ interface at this Reynolds number (fig. 3). Assessing the resolved fraction of turbulent mean skin friction by means of the FIK identity [START_REF] Fukagata | Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows[END_REF] [7] [START_REF] Deck | Zonal Detached Eddy Simulation (ZDES) of a spatially developing flat plate turbulent boundary layer over the Reynolds number range 3 150 ≤ Re θ ≤ 14 000[END_REF] shows that more than 90 % of the turbulent contribution is resolved at Re θ = 13 000 with the log layer interface setting [START_REF] Renard | Improvements in Zonal Detached Eddy Simulation for Wall Modeled Large Eddy Simulation[END_REF], a figure that increases with the Reynolds number. With the lower interface setting y + interface = 3.9 √ Re τ however, streamwise oscillations of mean skin friction are visible (fig. 4). This problem is strongly reduced by a smooth RANS/LES interface function f δ [START_REF] Renard | Improvements in Zonal Detached Eddy Simulation for Wall Modeled Large Eddy Simulation[END_REF] as illustrated in fig. 4, so that the formulation of the characteristic length scale of the SA turbulence model used for ZDES mode III becomes, as detailed in [START_REF] Renard | Improvements in Zonal Detached Eddy Simulation for Wall Modeled Large Eddy Simulation[END_REF]:

dIII DES = (1 -f δ ) • d w + f δ • min (d w ,C DES ∆ vol ) ; ∆ vol = (∆ x∆ y∆ z) 1/3
(1)

f δ (α) =      0 if α ≤ -1 1 1+exp -6α 1-α 2 if -1 < α < 1 1 if α ≥ 1 α = d w -d interface w (x center ) 0.1d interface w (x center ) (2)
Fig. 4 Smooth interface function f δ and mean skin friction evolution.

A few open questions related to the logarithmic layer

Mean skin friction prediction by ZDES is quite satisfactory (fig. 4), but some undesirable features may still be seen in the turbulent profiles (fig. 5). The innerscaled mean velocity profile deviates from the logarithmic law to an extent depending on the interface setting. Among the three heights considered in fig. 5, y interface = 0.1δ provides the best results. Associated with this deviation is a possible overestimation of the streamwise turbulent intensity near the RANS/LES interface (fig. 5). The spectral content of the excess of streamwise velocity fluctuations with y + interface = 3.9

√

Re τ is located right below the RANS/LES interface at large wavelengths (fig. 6), and is reminiscent of the stronger 'superstreaks' described in the early WMLES use of DES (e.g. [START_REF] Keating | A dynamic stochastic forcing method as a wall-layer model for large-eddy simulation[END_REF]). The better experimental agreement of the spectrum with y interface = 0.1δ has already been emphasized in [START_REF] Deck | Zonal Detached Eddy Simulation (ZDES) of a spatially developing flat plate turbulent boundary layer over the Reynolds number range 3 150 ≤ Re θ ≤ 14 000[END_REF] and [START_REF] Renard | On the interface positioning in a Zonal Detached Eddy Simulation (ZDES) of a spatially developing flat plate turbulent boundary layer[END_REF], as well as some very-large-scale energy deficit in the outer layer [START_REF] Renard | On the interface positioning in a Zonal Detached Eddy Simulation (ZDES) of a spatially developing flat plate turbulent boundary layer[END_REF] which remains unexplained to date. In order to better understand the nature of the excessive highwavelength fluctuations, their convection velocity is evaluated in §5. Indeed, if these fluctuations were quite unphysical, their convection velocity could even be totally different from the expected turbulent dynamics, which would be visible in the spectral convection velocity. The high-wavelength excess of power spectral density below the y + interface = 3.9 √ Re τ RANS/LES interface (fig. 6) is further investigated here by evaluating the wavelengthdependent convection velocity of the resolved fluctuations of streamwise velocity in this region of the spectrum. The method for the spectral assessment and the associated reconstruction of the spatial spectrum from time signals in the spatially developing boundary layer is detailed in [START_REF] Renard | On the scale-dependent turbulent convection velocity in a spatially developing flat plate turbulent boundary layer at Reynolds number Re θ = 13 000[END_REF] (inspired by a dual method [START_REF] Del Álamo | Estimation of turbulent convection velocities and corrections to Taylor's approximation[END_REF]). The frequency-dependent convection velocity U c ( f ) and the correlation coefficient γ u ( f ) describing the degree of validity of Taylor's frozen turbulence hypothesis are given by:

U c ( f ) = - 2π f S uu ( f ) Im S u ∂ x u ( f ) and γ u ( f ) = Im S u ∂ x u ( f ) S uu ( f ) S ∂ x u ∂ x u ( f ) (3)
The convection velocity U c ( f ) is presented for both interface settings in fig. 7. The relevancy of this information is confirmed by the correlation coefficient plotted in fig. 7, which is close to 1 for small scales (γ u ( f ) = 1 would be encountered in pure constant convection of perfectly frozen turbulence), and has sufficiently high values even at large wavelengths. The convection velocity increases with wall distance, as expected, and no grossly unphysical value can be seen including in the high-wavelength energy site below the RANS/LES interface. This implies that the reported excessive streamwise velocity fluctuations are not travelling at a velocity much different from what is expected for this energy site, discarding the possibility that they could be spurious fluctuations travelling at a quite unphysical velocity. The locus where the U c ( f ) convection velocity matches the local mean velocity, U c ( f ) = U , represented in solid line on top of the streamwise velocity spectra in fig. 8, may be called the 'critical layer' because of the analogy with stability analysis (where the maximum amplitude of the perturbation can be close to the locus where its phase speed coincides with the mean velocity). In fig. 8, the 'critical layer' coincides with the λ x ≈ δ energy site with both interface settings. In the case of a WRLES, this is even true for all three energy sites (hairpin packets, inner site and superstructures [START_REF] Renard | On the scale-dependent turbulent convection velocity in a spatially developing flat plate turbulent boundary layer at Reynolds number Re θ = 13 000[END_REF]). As for the high wavelengths below the RANS/LES interface in both WMLES simulations of fig. 8, the 'critical layer' is on the contrary located above the energy sites themselves. This suggests that the high-wavelength energy site of u with excessive levels for y + interface = 3.9

√ Re τ may be a footprint of coherent structures dynamically rooted higher in the boundary layer, near the 'critical layer'. Indeed, if the high wavelength energy site had its own dynamics, one would expect its convection velocity to be close to the mean velocity at its own wall distance rather than higher. Although explicit proof is still needed, fig. 8 strongly suggests that the observed excess of large-scale streamwise velocity fluctuations with y + interface = 3.9 √ Re τ actually is the footprint of a more physical dynamics located higher in the boundary layer. Whether this footprint may be removed without an active forcing is still an open question, probably related to the reduction of the logarithmic law deviation and to the resolved very-large-scale energy deficit in the outer layer. 6 Outlook ZDES Mode III has been analysed for WMLES of a ZPG flat-plate boundary layer over a wide Reynolds number range 3 150 ≤ Re θ ≤ 14 000. In the fully developed region, mean skin friction is predicted within 5 % of the experiments, using only 30 • 10 6 points (800 • 10 6 are required for a WRLES of the same test case also using ZDES mode III). The resolved fraction of Reynolds shear stress, which indicates whether the simulation is RANS or LES, is a monotonous function of wall distance close to 1 in the outer layer (both are satisfying properties). With the RANS/LES interface set at the centre of the logarithmic layer, the resolved fraction of turbulent mean skin friction increases with the Reynolds number and is greater than 90 % at Re θ = 13 000. A smooth RANS/LES interface function successfully reduces the streamwise friction oscillations with the lower interface setting. Several issues still arise in the logarithmic layer, with a deviation of the mean velocity profile, a very-large-scale turbulence deficit in the outer layer and an excess of highwavelength streamwise velocity fluctuations below the RANS/LES interface with y + interface = 3.9 √ Re τ . The latter problem has been analysed in more detail by assessing the wavelength-dependent convection velocity of the streamwise velocity fluctuations. The results suggest that the observed excessive energy is a footprint of a physical mechanism located higher in the boundary layer, rather than an autonomous artifact. This demonstrates the interest of using spectral analysis to get a better insight into the resolved field and its physical nature. To limit the high-wavelength footprint, properly setting the RANS/LES interface height is required, but the possibility to reduce it further without resorting to an active forcing is still an open question, probably related to the reduction of the log law deviation and of the very-large-scale energy deficit in the outer layer. Solving these issues on the generic high Reynolds number flat plate test case appears as a mandatory step before the WMLES technique is adapted to curvilinear complex geometries, since they affect very large wavelengths associated to key turbulent phenomena (e.g. superstructures) specific to the high Reynolds numbers characterising aerospace applications.

Fig. 1

 1 Fig.1Reynolds number impact on the pre-multiplied spectra k x G uu (k x )/u 2 τ reconstructed with a correlation-based convection velocity at Re θ = 5 200 (left) and Re θ = 13 000 (right). WRLES simulation using ZDES mode III (see[START_REF] Deck | Large scale contribution to mean wall shear stress in high Reynolds number flat plate boundary layers up to Re θ = 13 650[END_REF] and[START_REF] Renard | On the scale-dependent turbulent convection velocity in a spatially developing flat plate turbulent boundary layer at Reynolds number Re θ = 13 000[END_REF]).

Fig. 2

 2 Fig.2Flow visualisation near Re θ = 13 000 with ZDES mode III in WRLES operation (left,[START_REF] Deck | Large scale contribution to mean wall shear stress in high Reynolds number flat plate boundary layers up to Re θ = 13 650[END_REF]), WRLES interpolated onto the WMLES mesh (middle), and in WMLES operation (right, with y interface = 0.1δ ). Isosurface u = 0.8U ∞ coloured by wall distance; numerical Schlieren (density gradient magnitude).

Fig. 3

 3 Fig. 3 Present ZDES mode III interfaces for WMLES and profile of resolved fraction of u v .

9 √ 9 √

 99 (a) Mean velocity profile. • Experimental data from [10]. -S-A RANS. ZDES, WMLES mesh (200 + /100 + ): -y + interface = 200; -y interface = 0.1δ ; -y + interface = 3.Re τ . Dashed lines: RANS/LES interfaces. (b) Normal Reynolds stresses. • Experimental data from [10]. --ZDES, WRLES mesh (50 + /12 + ). ZDES, WMLES mesh (200 + /100 + ): -•-y interface = 0.1δ , -y + interface = 3.Re τ . Dashed lines: RANS/LES interfaces.

Fig. 5 Fig. 6 9 √

 569 Fig. 5 Velocity and normal Reynolds stresses profiles at Re θ = 13 000

Fig. 7 9 √ 2 τ

 792 Fig. 7 Spectral convection velocity U c ( f ) (3) and associated correlation coefficient γ u ( f ) (3) at Re θ = 13 000 with y interface = 0.1δ (left) and y + interface = 3.9 √ Re τ (right). Isolines of k x G uu (k x )/u 2 τ

Fig. 8 9 √

 89 Fig. 8 Premultiplied streamwise velocity spectra at Re θ = 13 000 with y interface = 0.1δ (left) and y + interface = 3.9 √ Re τ (right). The solid line represents the U c ( f ) = U locus ('critical layer').

Acknowledgements

The authors wish to thank all the people involved in the past and present evolution of the FLU3M code. Romain Laraufie and Pierre-Élie Weiss are warmly acknowledged for very stimulating discussions. The fine mesh WRLES computation was made thanks to the HPC resources from GENCI-CINES (Project ZDESWALLTURB, Grant 2012-[c2012026817]).