Antoine Joulain
email: antoine.joulain@airbus.com

Damien Desvigne
email: damien.desvigne@airbus.com

David Alfano
email: david.alfano@airbus.com

Thomas Leweke
email: thomas.leweke@irphe.univ-mrs.fr

Numerical investigation of the reliability of wind-tunnel wall corrections applied to measurements of wingtip flow

McAlister and Takahashi [2] is investigated at an uncorrected chordbased Reynolds number Re = 1.6 × 10 6 , Mach number M = 0.131 and angle of attack α = 12 • .

I. Introduction

H ELICOPTER aerodynamics is strongly influenced by the vortices generated from the rotor blade tips. A literature survey highlights the lack of local blade tip flow measurements, mainly due to the complexity of the aerodynamic phenomena involved and the difficulty of measuring in a small region of interest. Fixed wings have been widely investigated experimentally and numerically to gain more insight into the tip vortex formation, the influence of the shape and the accuracy of the numerical codes (see, e.g. Brocklehurst and Barakos [START_REF] Brocklehurst | A Review of Helicopter Rotor Blade Tip Shapes[END_REF] and references therein). The database of McAlister and Takahashi [START_REF] Mcalister | NACA 0015 Wing Pressure and Trailing Vortex Measurements[END_REF] includes detailed measurements of the vortex roll-up in the vicinity of the wing tip, as well as vortex characteristics during the near-field propagation. It is one of the very few published experimental campaigns considering Reynolds numbers of more than one million, as well as the sensitivity to the tip shape, the Reynolds number and the angle of attack. Moreover, measurements are rectified for meandering, and corrections are proposed to account for wind-tunnel wall interference. In spite of its wealth, this database is used surprisingly rarely as a reference test case to validate numerical methods.

Lim [START_REF] Lim | Numerical Study of the Trailing Vortex of a Wing With Wing-Tip Blowing[END_REF] used the proposed wall corrections to simulate a free-air rounded-wing tip configuration without representing the overall experimental setup. The Thin-Layer compressible Navier-Stokes equations (TLNS) were solved with a second-order scheme and an algebraic turbulence model. The grid extended 8 chords downstream of the trailing edge and 6 chords around the profile, and was refined in the spanwise direction near the tip. The solution was in agreement with the measurements, but the leading-edge upper-surface suction peak and the tip vortex pressure footprint were not captured. Due to computational speed and memory constraints, no grid dependence study was undertaken. According to the author, the simulation could be improved in a number of ways: by increasing the mesh density in areas of high velocity gradients, performing a grid convergence study, extending the domain dimensions, using Reynolds-Averaged Navier-Stokes (RANS) instead of TLNS equations and by using a more physical turbulence model. The relevance of the wall corrections was not called into question.

Kamkar and Wissink [START_REF] Kamkar | Automated Off-Body Cartesian Mesh Adaptation for Rotorcraft Simulations[END_REF] used McAlister and Takahashi's database [START_REF] Mcalister | NACA 0015 Wing Pressure and Trailing Vortex Measurements[END_REF] to perform a RANS simulation of the square-tip test case in free air, without wall corrections. An unstructured near-body grid was coupled with a structured off-body grid system. Adaptive Mesh Refinement, based on the Q-criterion [START_REF] Jeong | On the Identification of a Vortex[END_REF], was performed on the offbody mesh and showed considerable improvements concerning the vortex convection. A difference of 15% for the velocity inside the vortex remained between the best calculation and the measurements, it was attributed to the dissipation of the unstructured near-body mesh and to the communication between unstructured and structured grids. The lack of wall corrections was not discussed, but represents probably a major contribution to the error.

The objective of the present work is to assess the accuracy of the wind-tunnel wall corrections published by McAlister and Takahashi [START_REF] Mcalister | NACA 0015 Wing Pressure and Trailing Vortex Measurements[END_REF]. To do this, a validated and efficient steady-state RANS method is used to simulate two-and three-dimensional configurations in free-air flow configurations. In this paper, the square-tip test case of

II. Computational Setup

The configuration considered in the present simulations consists of a constant-chord NACA 0015 wing with a square tip, bounded at the root by a symmetry plane. The wing aspect ratio is small, it is therefore assumed rigid and free of aeroelastic deformations. Two coordinate systems are defined in the same way as for the experimental setup (presented in Section III). The first one is used to study forces and moments acting on the wing: the rand ζ-axes extend respectively from the experimental root to the tip and from the leading edge to the trailing edge, the origin being at the root leading edge of the experimental geometry. The Eiffel frame (x, y, z) is employed to follow the tip vortex: the x-axis is aligned with the (horizontal) inflow direction; the y-axis extends from the tip to the root of the wing and the z-axis is vertical; moreover the origin is located at the center of the vortex core.

II.A. Numerical Method

The ONERA CFD code elsA [START_REF] Cambier | The Onera elsA CFD Software: Input From Research and Feedback From Industry[END_REF] is used in this study. The solver is based on a cell-centered, finite-volume approach. Assuming a steady flow field, the compressible RANS equations are solved in twodimensional (2D) and three-dimensional (3D) configurations on a multi-block structured grid. A fully turbulent flow is considered, without boundary-layer transition.

The governing equation system is closed with the one-equation model of Spalart and Allmaras [START_REF] Spalart | A One-Equation Turbulence Model for Aerodynamic Flows[END_REF]. Based on the Boussinesq assumption, this formulation was initially designed for the simulation of wallbounded flows. In order to reduce the production of eddy viscosity in areas where the vorticity is higher than the strain rate (e.g. inside vortex cores), the rotation and streamline curvature correction proposed by Spalart and Shur [START_REF] Spalart | A One-Equation Turbulence Model for Aerodynamic Flows[END_REF] is applied.

The convective fluxes of the mean flow equations are discretized using the second-order central scheme of Jameson, Schmidt and Turkel [START_REF] Jameson | Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes[END_REF]. Since this scheme is non-dissipative and unstable, a matrix artificial dissipation is introduced. The fourth-order coefficient κ (4) dampens the high-frequency oscillations in the bulk of the computational domain and is important for stability and convergence to a steady state. Typical values for κ (4) are in the range 0.016 to 0.032 [START_REF] Swanson | On Some Numerical Dissipation Schemes[END_REF]. In order to reduce the amount of dissipation being introduced and to improve the accuracy, κ (4) is taken as 0.016. The convective fluxes of the turbulence equations are discretized using a second-order Roe scheme [START_REF] Roe | Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes[END_REF]. All diffusive flux gradients are calculated with a five-point central scheme. A first-order backward-Euler scheme updates the steady-state solution and the LU-SSOR (Lower-Upper Symmetric Successive Over-Relaxation) scheme [START_REF] Yoon | An LU-SSOR Scheme for the Euler and Navier-Stokes Equations[END_REF] is employed to speed up convergence.

The resulting flow solver is implicit and stable, and high values of the Courant-Friedrichs-Lewy (CFL) number can be reached. The CFL number is linearly ramped up from 1 to 10 over 100 iterations, in order to avoid divergence during the transient phase. The L 2 norm-based residual of the total energy per unit volume, ℜ, is used to measure the convergence of the simulations. 1

II.B. Computational Grid

The structured grids are generated using the ANSYS ICEM-CFD software, and all lengths are normalized by the wing chord c. The initial mesh is designed for industrial use and is universally applicable, without prior knowledge of the final solution. In particular, the vortex trajectory is not used to align the main grid axis and to refine the mesh in the zone covering the vortex core. This choice allows a wide variation of angle of attack, free-stream velocity and geometry.

The mesh results from an exhaustive grid-independence study concerning each construction parameter (documented in Ref. [START_REF] Joulain | Aerodynamic Simulations of Helicopter Main-Rotor Blade Tips[END_REF]). A Ctopology surrounds the 2D NACA 0015 profile and an H-topology covers the downstream zone. In the spanwise direction, an H-topology is also chosen to match the square wing tip. The computational domain extends up to a distance of 200c in all directions from the tip in order to minimize the influence of boundary conditions. Thus the numerical wing has a span of 200c. The difference between experimental and numerical wing spans is not detrimental to the study of the vortex roll-up in the vicinity of the tip, as the root circulation is transferred into the trailing sheet.

The 2D mesh around the NACA 0015 profile is constructed as follows. In the streamwise direction, the leading-edge grid spacing is equal to 10 -4 c and the trailing-edge grid spacing is 2 × 10 -4 c. The blunt trailing edge (of thickness 3.15 × 10 -3 c) is finely discretized with a grid spacing of 8.3 × 10 -6 c at the corners. The mesh distribution around the profile follows geometric progressions starting from each specified grid spacing. The common ratio of a geometric progression is called expansion ratio. The expansion ratio on the profile is lower than 1.06. In the wall-normal direction, the first grid spacing is set to 8.3 × 10 -6 c for a dimensionless wall distance (y + , see e.g. Ref. [START_REF] Tennekes | A First Course in Turbulence[END_REF]) around unity at the first computational nodes. At 12 • incidence and Reynolds number 1.5 × 10 6 , the computed y + is maximal at the suction peak with a value of 1.5, and it does not exceed 0.5 on the lower side of the profile. The wall-normal expansion ratio is set to 1.15 and is not relaxed away from the profile in order to preserve the orthogonality of the cells. Downstream of the trailing edge, the first grid spacing is equal to the trailing-edge grid spacing and an expansion ratio of 1.1 is applied. The distribution on the outer boundary is manually adapted to maximize the orthogonality of the mesh at the wall. The resulting 2D mesh contains 7 × 10 5 points.

The 3D mesh is constructed by stacking 2D meshes along the raxis. The boundary layer developing around the square tip is simulated with a spanwise tip spacing of 5 × 10 -5 c. The maximum value of the dimensionless wall distance y + reaches 8 and is located in the vicinity of the leading edge. A spanwise expansion ratio of 1.01 is imposed throughout the fluid domain, as well as from the tip to the root of the wing. In the fluid domain, the gap resulting from the 2D mesh stacking is filled with a half-butterfly mesh (O-grid mesh), which inevitably induces two lines of skewed cells near the fictitious leading edge. The wall-normal grid spacing and expansion ratio are used in the gap domain. The final mesh contains 4.4 × 10 7 points and is split into 137 blocks to enable parallel processing. The values of the grid parameters are summarized in Table 1. The wing surface is modeled as an adiabatic viscous wall (zero heat-flux). The outer boundary supporting the root of the wing is a symmetry plane, whereas a far-field condition is applied to all other external boundaries.

III. Experimental Database

McAlister and Takahashi's [START_REF] Mcalister | NACA 0015 Wing Pressure and Trailing Vortex Measurements[END_REF] wing consisted of a constant and untwisted NACA 0015 profile with a square tip. The chord (c) and semispan (R) were respectively 0.52 m (1.7 ft) and 1.7 m (5.6 ft). The width (w) and the height (h) of the test section were 3 m (10 ft) and 2.1 m (7 ft). The wing was mounted on a 6.4 cm (2.5 in) thick supporting end plate extending from floor to ceiling. In the lateral direction, the tip of the wing and the supporting end plate were positioned respectively at 1 m (3.3 ft) and 0.3 m (1 ft) from the wind tunnel walls. A cylindrical tube fairing was placed between the supporting end plate and the wall. In order to perform 2D measurements, a second end plate was positioned against the tip, preventing the development of a trailing vortex. The transition of the boundary layers was not forced.

Wing surface pressure (coefficient C p ) was measured at 320 stations, with a denser distribution near the leading edge and the tip. The measurement section nearest the tip was located at a distance of 2% of the chord c, i.e. at r/R = 0.994. Lift (C l ), pressure-drag and pitching moment coefficients were calculated from a trapezoidal-rule integration of the pressure distribution. The pitching moment coefficient is defined about the quarter-chord and is taken as positive when the angle of attack is increasing. Results are published in the Eiffel frame (with respect to the undisturbed flow). A two-components laser velocimeter is used to measure the vertical (V z ) and the axial (V x ) velocity profiles across the trailing vortex along the y-axis. Measurements are made at streamwise locations from 0.1c to 6c behind the wing.

III.A. Blockage Correction

During the experiment, the reference velocity is obtained from a Pitotstatic probe placed upstream in the test section. The experimental assembly generates a blockage resulting in a higher velocity in the region where the airfoil is located. The uncorrected reference velocity V ∞,u (and consequently the Mach number, Reynolds number and all aerodynamic coefficients) has to be corrected according to

V ∞ = (1 + ε)V ∞,u (1)
The value of the blockage factor ε, in 2D and 3D configurations, is estimated using a simple formula based on the area reduction induced by each object in the tunnel [START_REF] Rae | Low-Speed Wind Tunnel Testing[END_REF]:

ε = b Object frontal area Test section area (2)
with b = 0.25 for the airfoil and b = 1 otherwise. The additional blockage resulting from the development of the tunnel boundary layers and the wing wake is not taken into account. According to the published geometry of the assembly, the total blockage factor, at an angle of attack α = 12 • , is ε = 0.06 in the 2D configuration and ε = 0.04 in the 3D configuration. The blockage factor of the airfoil is weakly dependent on the angle of attack and represents 13% and 20% of the total blockage in 2D and 3D, respectively. End plates are the major contributors, with 70% of the total blockage in the 2D configuration (two end plates) and 54% in the 3D configuration. For the former, this leads to a reduction of the force and moment coefficients by about 12%. Velocity profiles reveal that far from the wing tip vortex (and the wing trailing sheet), the streamwise velocity tends neither to the uncorrected nor to the corrected reference velocity, but converges to a value between 1.1 V ∞,u (at x t /c = 0.1) and 1.07 V ∞,u (at x t /c = 4). The boundary layers developing on the supporting plate and the tunnel walls, as well as the wake, may induce an additional blockage and an increase of the local velocity downstream of the profile. However, the observed deviation of the axial velocity from the corrected reference value is rather erratic and does not increase with downstream distance. A calibration error of the laser velocimeter could be responsible for such discrepancies. Two methods can be used to correct the vertical and axial velocities: the first is to increase the blockage factor (up to 0.1 at x t /c = 0.1), and the second to apply the blockage factor calculated from Equation ( 2) and shift the corrected measurements to recover V ∞ far from the vortex. The two methods give similar results, and the first one is retained.

III.B. Lift Interference Correction

The walls of the closed test section confine the airflow and distort the streamlines around the lifting body.

In the 2D configuration, Lock's [START_REF] Lock | The Interference of a Wind Tunnel on a Symmetrical Body[END_REF] method for taking this effect into account consists in replacing the lifting airfoil by a single vortex at the center of pressure. The floor and ceiling of the tunnel are mathematically represented by an infinite series of image vortices, in order to satisfy the absence of normal flow at the walls. The angle of attack α and the lift coefficient C l of the profile are modified by the velocity induced by these image vortices. Assuming a profile centered in the test section, a short chord c relative to the tunnel height h and a small angle of attack, the corresponding corrections were given by Allen [START_REF] Allen | Wall Interference in a Two-Dimensional-Flow Wind Tunnel, with Consideration of the Effect of Compressibility[END_REF] as:

α = α u + 180 π πc 2 96βh 2 (C l,u + 4C m,u ) and C l =       1 - 1 3 πc 4βh 2       C l,u with (3)
β = 1 -M 2 u
The low Mach numbers considered here allow to assume an incompressible flow (compressibility factor β = 1). Due to the small value of the ratio c/h (0.25), the lift interference correction in the 2D configuration is very small: the angle of attack is increased by 1% and the lift coefficient is decreased by 1.6%.

In the 3D configuration, the half-model is treated as a complete wing in a tunnel with twice the cross section, with the side-wall as a symmetry plane. The lifting wing is replaced by a semi-infinite vortex pair trailing from the tips. The walls of the tunnel are now represented by a doubly-infinite series of vortex images. Assuming again a small wing compared to the dimensions of the tunnel, only the angle of attack is modified according to [START_REF] Garner | Subsonic Wind Tunnel Wall Corrections[END_REF]

α = α u + δ E 180 π 1 + cδ 1 2βhδ 0 A A t C l,u (4)
where A is the planform area of the semi-span wing (Rc), A t the crosssectional area of the tunnel (wh), and where δ E , δ 0 and δ 1 depend only on the geometric parameters 2w/h and R/w. Detailed expressions and charts can be found in Ref. [START_REF] Garner | Subsonic Wind Tunnel Wall Corrections[END_REF] and Ref. [START_REF] Glauert | Wind Tunnel Interference on Wings, Bodies and Airscrews[END_REF]. For the present experiment, with 2w/h = 2.86 and 2R/b = 0.56, these parameters are estimated as δ E = 0.05, δ 0 = 0.19 and δ 1 = 0.42, respectively. Assuming an incompressible flow (β = 1), the correction in Equation ( 4) is directly proportional to the lift coefficient and increases the incidence by 4.3% at 12 • . The trajectory of the tip vortex is also influenced by the walls of the tunnel. In free air, the vortex pair generated by a lifting wing is deflected downward by mutual induction. In the tunnel, the walls, or the equivalent doubly-infinite series of images, generate induced velocities acting on the tip vortex. The wing and trailing vortex are centered in the vertical direction in the tunnel, thus the interference concerning the horizontal displacement of the tip vortex is very small. On the contrary, in the lateral direction the tip of the wing and the trailing vortex are closer to the opposite side wall than to the supporting end plate. Thus the lift interference on the vertical displacement is quite substantial. Due to this up-wash the tip vortex is actually measured to move upward, which is not consistent with the behavior in free air.

IV. Comparison Between Simulation and Experiment

IV.A. Two-Dimensional Flow

The 2D test case of McAlister and Takahashi [START_REF] Mcalister | NACA 0015 Wing Pressure and Trailing Vortex Measurements[END_REF] at Re = 1.5 × 10 6 (M = 0.124) is calculated for angles of attack in the range 0 • ≤ α ≤ 14 • , in steps of 1 • . The blockage correction increases the Reynolds number to 1.6 × 10 6 (M = 0.131). The lift interference correction is taken into account in the CFD simulations.

In order to study the convergence history, 100,000 iterations are performed at a (corrected) incidence of α = 12.13 • . The residual ℜ drops by six orders of magnitude. After 12,000 iterations, the variation of lift and pressure drag is less than 1% of the converged values. 20,000 iterations are required to reach an error below 0.1%. Approximately three hours are needed to achieve 20,000 iterations on six cores of Intel Xeon E5-2697 v2 processors at 2.7 GHz interconnected with an Infiniband FDR network and with 48 Go of RAM.

The dependence of the lift coefficient on angle of attack is plotted in Fig. 1. Its variation along the span of the wing in the experiments appears as error bars on the symbols. In the case of a purely 2D flow, no spanwise variation is expected. The observed deviation depends weakly on the angle of attack in the range 0 ≤ α ≤ 10 • and can be interpreted as the experimental measurement scatter. For α > 10 • , this variation increases, indicating the additional influence of a 3D stall phenomenon.

Figure 1 reveals a significant difference between the uncorrected lift measurements and the simulation results. At α = 12 • , this difference reaches 16%. The blockage correction greatly improves the agreement, the deviation at α = 12 • being reduced to 3%, and even to 1% when applying the lift interference correction. The agreement is poor at α = 14 • . Experimentally, the 2D assumption at this incidence is less justified, because the variation along the span is high and the flow is probably stalled. According to the review of 2D experimental databases published by McCroskey [START_REF] Mccroskey | A Critical Assessment of Wind Tunnel Results for the NACA 0012 Airfoil[END_REF], the measurement of maximum lift at low Mach number suffers from a high dispersion, partly due to wind tunnel wall effects. Concerning simulation aspects, the RANS equations have previously shown low efficiency with the simulation of 2D stalled flow [START_REF] Szydlowski | Simulation of Flow Around a NACA0015 Airfoil for Static and Dynamic Stall Configurations Using RANS and DES[END_REF][START_REF] Moulton | The Role of Transition Modeling in CFD Predictions of Static and Dynamic Stall[END_REF]. One of the main causes is the inadequacy of the boundarylayer transition model to simulate leading-edge laminar-bubble separation and expansion up to stall.

IV.B. Three-Dimensional Flow

The accuracy of the 3D corrections is now investigated by a comparison between the numerical simulation and the 3D experimental database of McAlister and Takahashi [START_REF] Mcalister | NACA 0015 Wing Pressure and Trailing Vortex Measurements[END_REF]. The square-wing tip test case is used at Reynolds number Re = 1.6 × 10 6 , Mach number M = 0.131 and angle of attack α = 12 • . The blockage correction (III.A) increases the Reynolds number to Re = 1.7 × 10 6 and the Mach number to M = 0.140. The lift interference correction (III.B) increases the angle of attack to α = 12.5 • .

In order to assess the convergence of the 3D solution, a simulation with 100,000 iterations was performed, requiring approximately 50 hours of calculation on 150 cores. During the first 40,000 iterations, the residual ℜ drops by four orders of magnitude. It then stagnates until the end of the calculation. The same trend is observed for all other conservative variables, including turbulent ones. The main cause for this stagnation is localized at the leading edge of the tip section. In this area, the geometric truncation produces sharp edges, responsible for flow separation and a destabilization of the solution. The residual, which is an integrated value over the whole domain, is polluted by this local fluctuation. Nevertheless, the low CFL number employed prevents the propagation of this instability beyond a few tenth of a percent of the chord from the tip leading edge.

The vortex generation process alters the pressure in the vicinity of the wing tip. The low-pressure footprint generated on the upper surface is responsible for additional lift, pressure drag and pitching moment peaks. In the vortex footprint, the three sectional coefficients converge very well, but at different speeds. After 20,000 iterations, the resulting C l reaches the converged value (obtained with the 100,000-iteration calculation) to within 0.25%. The convergence of the drag and pitching moment coefficients is slower, and the results are within 0.4% and 0.6% of the converged values, respectively. Far away from the tip, in the inner part of the wing, the convergence of the aerodynamic coefficients is identical to the purely 2D configuration presented in Section IV.A.

From the blade root to the blade tip, and in particular from r/R = 0.88 to the tip (Fig. 2), the corrected experimental lift coeffi- cient is in good agreement with the calculated one. Similar agreement is obtained for the pressure drag and the pitching moment coefficients.

y /c V z / V ∞ -0.
At r/R = 0.370 and r/R = 0.974, the numerical pressure coefficient profiles and the corrected measurements are in good agreement, which demonstrate the validity of the wall corrections. At r/R = 0.994 (Fig. 3), the three upper-side suction peaks are found at the same position along the chord. The two pressure peaks at the leading-edge (upper side and lower side) are in good agreement. However, the simulation overestimates the amplitude of the first (at ζ/c ≈ 0.3) and second (at ζ/c ≈ 0.8) vortex footprints by 9% and 14%, respectively. The numerical results are always located between the uncorrected and the corrected measurements. The deviation on the lower side of the wing is surprising, it could be due to the application of an excessive blockage correction to the measurements. Considering the rough approximation of Eq. ( 2), the deviation remains acceptable.

Numerically, the "main vortex" center is identified, from the trailing edge up to 6 chords behind the wing by the maximum value of the Q-function [START_REF] Jeong | On the Identification of a Vortex[END_REF]. From the trailing edge up to 0.5c downstream, the simulated and measured main vortex trajectories are in good agreement.

Beyond 1 chord downstream of the trailing edge, the horizontal displacements slightly diverge and result in a 10% deviation at 6 chords. In the vicinity of the wing, the measured vertical displacement is not influenced by the wind tunnel walls and matches the simulation result. From 1 chord downstream, the experimental values are clearly influenced by the tunnel walls and are not comparable to a free-air simulation.

Velocity profiles are extracted on a horizontal line passing through the main vortex center, in order to mimic the experimental procedure. The measured profiles are corrected with a suitable blockage factor (see Section III.A), in order to recover V x /V ∞ = 1 far from the vortex and the wing trailing sheet. At 0.1 chord downstream of the trailing edge (Fig. 4), the vertical velocity amplitude is lower than unity and the application of the correction has little influence. The two maxima observed on the vertical velocity profile (at y/c ≈ -0.09 and -0.02) are well located. The simulation overestimates the first maximum by 20%, compared to the corrected measurement. A precise comparison cannot be made concerning the maximum and minimum vertical velocities; nevertheless, the experimental values and the numerical result are consistent. In particular, the small double inflection seen at y/c ≈ 0.02 is present in both cases. At y/c ≈ 0.07, the simulation exhibits a local deviation of 25% with respect to the corrected measurement. At 0.2 chord downstream of the trailing edge (Fig. 5), the corrected measurements and the calculated axial velocity profile are in good agreement. The maximum amplitudes are identical, the large lowvelocity region between y/c ≈ -0.12 and -0.04 is similar, and the small low-velocity region at y/c ≈ 0.06 is visible. Contrary to the measurements, the numerical solution exhibits a second peak at y/c ≈ 0.04.

V. Conclusions

To conclude, concerning the 2D test case at Reynolds number 1.6 × 10 6 and Mach number 0.131, good agreement is found between the numerical solution and the corrected measurements. On the one hand, the numerical is fast and gives accurate solutions, as long as the airfoil does not approach stall. On the other hand, the blockage correction and the lift interference correction given by Equations ( 2) and (3) are well suited and reveal the high quality of the database. Except near stall angles, where the 2D assumption becomes invalid, the corrected mean values of pressure, lift and pitching moment coefficients match the numerical results.

Concerning the 3D square-wing tip test case at Reynolds number Re = 1.6 × 10 6 , Mach number M = 0.131 and angle of attack α = 12 • , the corrected experimental measurements and the numerical solution are in good agreement regarding the mean aerodynamic coefficients on the wing and the mean vortex characteristics in the near field (up to 1 chord downstream of the trailing edge). The basic wall corrections proposed by McAlister and Takahashi [START_REF] Mcalister | NACA 0015 Wing Pressure and Trailing Vortex Measurements[END_REF] are found to be necessary and reliable. They produce results consistent with free-air simulations, even if the employed blockage factor appears slightly too high for the measurements close to the tip. Between the trailing edge and 0.5 chord behind the wing, the simulated vortex trajectory agrees well with the measurements, even in the vertical direction, where the influence of the tunnel walls is known to be strong. In order to recover the reference velocity far from the vortex and the wing trailing sheet, the vertical and axial velocity measurements are corrected with an ad hoc method. A good match is found between corrected experiment and simulation for the vortex roll-up, concerning the amplitude and location of the velocity peaks, as well as the medium-and high-frequency variations of the velocity profiles.

Deviations between numerical solution and measurements are probably related to the use of steady-state simulations. Nevertheless, this efficient numerical method allows a detailed physical analysis of the vortex roll-up around the square wing tip in order to understand the origin and development of the multiple variations observed in the pressure and velocity profiles. The same numerical method is used in Ref. [START_REF] Joulain | Aerodynamic Simulations of Helicopter Main-Rotor Blade Tips[END_REF] to compute different test cases of McAlister and Takahashi's database [START_REF] Mcalister | NACA 0015 Wing Pressure and Trailing Vortex Measurements[END_REF], including variations of tip shape, Reynolds number and angle of attack variations.

Figure 1 .

 1 Figure 1. Lift coefficient as function of angle of attack for the 2D configuration at Re = 1.6 × 10 6 and M = 0.131. numerical solution (--), uncorrected (•) and corrected ( ) experimental data from McAlister and Takahashi [2].

Figure 2 .

 2 Figure 2. Sectional lift coefficient along the span in the vicinity of the tip. Numerical simulations (--), uncorrected (•) and corrected ( ) experimental data from McAlister and Takahashi [2].

Figure 3 .

 3 Figure 3. Pressure coefficient along the chord at r/R = 0.994. Numerical simulation (--), uncorrected (•) and corrected ( ) experimental data from McAlister and Takahashi [2].

Figure 4 .Figure 5 .

 45 Figure 4. Vertical velocity profiles across the vortex core at 0.1 chord downstream of the trailing edge. Numerical simulation (--), uncorrected (•) and corrected ( ) experimental data from McAlister and Takahashi [2].

Table 1 .

 1 Grid parameters

	Domain dimension	(400c) 3
	Leading-edge streamwise spacing	10 -4 c
	Trailing-edge streamwise spacing	2 × 10 -4 c
	Profile streamwise expansion ratio	1.06
	Wall-normal first spacing	8.3 × 10 -6 c
	Wall-normal expansion ratio	1.05
	Downstream first spacing	2 × 10 -4 c
	Downstream expansion ratio	1.1
	Spanwise tip spacing	5 × 10 -5 c
	Spanwise expansion ratio	1.01


Claude Domergue

Jean-Marc Fabre

    Once Upon a Time, a Shaft Furnace... The Standard Bloomery Furnace (1st Century B.C.) at Les Martys (Southern France)

The bloomery plant of 'Les Martys' , situated in the Montagne Noire (Aude, Southern France), is one of the main iron smelting sites in the Roman world.

An Italian iron smelting project at Les Martys …

As early as 80/70 B.C., an iron smelting plant was treating the hitherto unexploited lodes of iron ore (gossans) on the south slope of the Montagne Noire. The concerned site coincides with the one currently occupied by the 'Domaine des Forges' , at an altitude of 2200 ft above sea-level, in the valley of the river Dure, among granite rocks and beech-trees. This rm bears many features characteristic of Italic culture (foodways, Pompeian mills).

It may be surmised that it originated in the only Italian iron smelting area, Populonia -the Isle of Elba, on the Etrurian coast, working in the course of the 2nd and 1st centuries B.C.

… with a smaller bloomery shaft furnace …

The shaft furnaces used there for iron smelting belong to a well known type : small size, with bowl dug into the earth, air duct at the back and slag tapping appliance. Now, in the oldest part of the Domaine des Forges, a small shaft furnace was found : F 33, with similar features to the furnace at Populonia-Isle of Elba ; it is tempting to draw a parallel with that unique exemplar.

… but here is the « standard » shaft furnace, constructed locally …

Indeed, 16 exemplars of another type of shaft furnace are available : bigger ones (from 2.30 to 2.50 m in height ; up to 1.90 m in length, and 1.60 in width ) and more bulky :

-base made of three big granite masses, -upper part made of small blocks of shale, gneiss or granite, -at the base, an opening temporary blocked by light masonry, topped by a curved lintel, with two strong granite piers, -a ventilation system composed of three slanting air ducts within the masonry, with cone-shaped tips, -slag-tapping, -withdrawing of the bloom without knocking o the built-up structure. Such is the typical shaft furnace of Les Martys in the 1st century B.C.. It appears that, in matters of wielding and yielding, the smaller Italic variety could not stand its own against a bigger type and, so, was dropped.

The standard bloomery furnaces generally went in twos, threes, and even in ranges of six. That type is a good illustration of the use of local materials : the heavy masses of granite with good thermic inertia, the sand and clay, the layers of shale and gneiss.

As regards its construction, this « standard » shaft furnace is a local product.

… yet of Iberian conception.

But, a detail in its conception betrays an Iberian in uence : the cone-shaped tips at the end of the air ducts. Except for Les Martys, such a component is only to be found in the shaft furnaces of La Juncada (Sierra Menera -Teruel), an ancient iron smelting site situated in Celtiberia, in Spain ; they have been dated as belonging to the 4th-3rd centuries B.C. ; but archeological research shows that iron smelting was carried on in the area -possibly with the same type of furnace -right through to the 1st c. A.D. ; that very iron whose quality was celebrated, at the end of that period, by the latin poet Martial, born at Bilbilis -now Calatayud -, a nearby town (Epigrams, IV, 55, 11-13).

As a conclusion, one may consider the standard shaft furnace as a mere inheritor of the Celtiberian shaft furnace, with greater capacity, three tip-ended air ducts instead of two, and stronger building materials. One should then overlook neither the excellence of Iberian mining, which was born and developed in what can be named the Eldorado of the Ancient world, nor the way the Roman capitalists used and improved it, rst in Iberia itself, in Gaul later. The Italian « invasion » of Spanish mines (as is highlighted in the text due to Diodorus of Sicily, Historical Library, 5, 36, 3), was later extended to Gaul, into which area they imported the Iberian skills, as is apparently exempli ed by the standard shaft furnace of Les Martys.

In memory of Radomir Pleiner

  , Les bas fourneaux de réduction du fer (Ier s. av. J.-C.) des Martys (Aude, France). Note additionnelle à Martys 2, Revue Archéologique de Narbonnaise 2017 (forthcoming). Fabre J.-M., Domergue C. et Dabosi F. (dir.), Le fer romain de la Montagne Noire. Martys 2 : les débuts. 25 années de recherches plurisdisciplinaires (1988-2013), Supplément à Revue Archéologique de Narbonnaise, 43, Montpellier 2016, 556 p. Villargordo Ros C., Polo Cutando P., Fabre J.-M., Coustures M.-P., Rico C., «Innovación sin desarrollo : el taller metalúrgico de la Juncada (Peracense, Teruel). Evidencias de la producción de hierro en los siglos IV-III A.C. en el ámbito celtibérico del área minera de Sierra Menera», Kobie, Anejos 13, 2014, p. 75-95. Voos O., «The Iron Production in Populonia», In G. Sperl (ed.), The rst iron in Mediterranean, PATC 21, Strasbourg, 1988, p. 91of slags = 34 000 t of iron between 80/70 B.C. to 260 A.D. C. Domergue et J.-M. Fabre, TRACES -UMR 5608 CNRS, Université Toulouse-Jean Jaurès lintel F 33

(

  English translation:Jean-Paul Débax, 2017)


Sandrine Maljean-Dubois
email: s.maljean-dubois@univ-amu.fr

Matthieu Wemaëre
email: matthieu@wemaere-avocats.eu

"Complex is beautiful". What role for the 2015 Paris Agreement in making the Effective Links within the Climate Regime Complex?

The 1992 United Nations Framework Convention on Climate Change (UNFCCC) 3 provides for the foundation of the international regime to fight against climate change. But it is widely acknowledged that it is neither efficient nor sufficient to tackle this challenge. As from 2000, a proliferation of policy initiatives outside this international climate regime has progressively questioned the centrality of the international governance on climate change as laid down by the UNFCCC.

Climate talks under the auspices of the UNFCCC for the adoption of a new accord in Paris in December 2015 at the 21st Conference of the Parties to the UNFCCC provided a unique opportunity to rethink the role and structure of the international climate regime within its own boundaries. In order to increase the level of ambition of climate action as soon as possible and in the future, it was of crucial importance to design the Paris Accord in a way that it coulb be complemented and enhanced through synergies with other initiatives, which may be developed in other fora of international cooperation.

This article analyses the role the Paris Agreement could play in achieving the defragmentation of the international governance on climate change, which could contribute to enhancing new cooperation dynamics, and to building a (more) consistent global climate law.

Introduction

Climate change is a highly complex policy challenge. Its causes cut across all economic sectors. Solutions require many different kind of policies in energy, infrastructure, finance and innovation, to name just a few. At the international level, the United Nations Framework Convention on Climate Change (UNFCCC) is widely seen as the central pillar of a broader 'regime complex', encompassing a number of formal and informal international policy processes.

Negotiations on a new climate agreement should be concluded under the UNFCCC by the end of 2015 in Paris. 4 Many countries expected these negotiations to produce a durable, legal agreement, which can structure climate cooperation in the long-term. But, regarding their difficulties to found a consensus, the Durban Platform gave birth to an a minima agreement in which the collective effort is the result of the aggregation of "nationally determined" contributions. The Parties themselves establish their contribution's level of ambition, at a national level, keeping in mind the collective objective of holding global warming well under 2°C. The COP will likely provide further guidance to the States as to how they determine their contribution 5 , but until now there has been no burden sharing of the implementation of this collective objective, as it had been the case pursuant to the Kyoto Protocol and in particular as between the fifteen countries of the European Union at the time, who had allocated between themselves a common objective of reducing their emissions by 8% 6 . The objective of holding temperatures laid down in the Agreement is however completely unrealistic based on our emissions' trajectories. This is established on an annual basis by the United Nations Environment programme in its report entitled The Emissions Gap, released before each COP. This report analyses the gap in terms of ambition until 2020 7 . Several studies have also analysed the aggregate effect of States' national contributions prior to the COP 21, including a study commissioned pursuant to the UNFCCC for 31 October 2014 8 . It concluded that, combined altogether, these contributions do not take us towards 2°, even less 1.5°, but rather, according to estimates, towards 3 or 3.5°C. This is undoubtedly progress compared to the 4 or 5 °C expected by so-called "business-as-usual" scenarios. Even though today 191 Parties representing 98% of global emissions have submitted their national contribution, we are still very far from the objective set out in the Paris Agreement and, beyond that, from the safe operating space of our planet 9 .

Thus, to improve the level of ambition now and in the future, it is fundamental that the Paris agreement could be supplemented or even fuelled by other initiatives, actions and policies, coming from other fora of international cooperation. This raises the question: what can the new agreement do in order to better forge effective synergies within the different elements of the climate regime, and to manage potential frictions? In a fragmented legal landscape (2), the Paris Agreement gives some new leverage tools for achieving the defragmentation of the international climate governance (3). 4 UNFCCC, Decision 1/CP.17 (2011), Establishment of an Ad Hoc Working Group on the Durban Platform for Enhanced Action.

5 CCNUCC, Secretariat, Parties' views regarding further guidance in relation to the mitigation section of decision 1/CP.21, FCCC/APA/2016/ INF.1, 7 October 2016, add.1, 18 October 2016. 6 This burden sharing was carried out by applying a basket of criteria established by the Utrecht University, based on the population, growth and energetic efficiency as well as opportunity or more political considerations. G. PHYLIPSEN, J. BODE, K. BLOK, H. MERKUS, B. METZ. A triptych sectoral approach to burden differentiation; GHG emissions in the European bubble, Energy Policy, n°26, pp. 929-943. 1998

From a fragmented governance landscape to regime complexes

The issue of fragmentation has gained more weight in recent times, as researchers and policy makers realise the complexity of climate change, and search for effective solutions. We can highlight three central reasons why the climate regime has long displayed this degree of fragmentation.

First, as mentioned above, climate change is a high complex, multi-sector, multi-scale problem. Addressing it effectively requires coordinated policy responses in many domains. Ongoing work by the OECD, for example, assesses the multiple policy response required at the national level from different sectoral policy processes: from energy policy, trade and competition policy, innovation policy, infrastructure planning, and financial regulation. The same principle holds at the international level. An effective response to climate change will inevitably require a complex, multifaceted response, combining the expertise and mandates of different policy processes.

Secondly, there has also been in the past a divergence of views between countries and researchers regarding appropriate processes. This has been particular manifest in the debate about multilateral versus mini-lateral approaches to international coordination. Today it is probably fair to say that this conflict is perhaps less fundamental, and that a majority of experts and policy makers see multilateral and mini-lateral as complementary. This can be seen in the so-called Workstream 2 process under the UNFCCC and the Lima-Paris Action Agenda, which aims to catalyse a range of International Cooperative Initiatives. 10 It is therefore being increasingly recognized that the UNFCCC is a core aspect of the global climate regime, but insufficient by itself.

Thirdly, international law is, by definition, a fragmented regime. Fragmentation arises logically from the principle of 'autonomy of treaties', according to which every treaty is independent of all other treaties. The fragmentation of the international legal order is even increasing, due to the twofold movement of expansion and diversification of international law. [START_REF]BIERMANN F. Planetary boundaries and earth system governance: exploring the links[END_REF] The situation is even worse in international environmental law, without a global environmental organization supervizing or even unifying the hundreds of autonomous institutional arrangements existing. 12 In international law, "normative conflict is endemic to international law" as stated by an International Law Commission's report. 13 The UNFCCC forms, of itself, already a fairly complex legal regime. The Convention, the Kyoto Protocol, the Cancun Accords and now the Paris agreement all represent significant albeit distinct developments of the climate regime. Nonetheless, overall the UNFCCC regime represents a relatively cohesive whole. In the past, it can be argued that the sharing of the workload between the UNFCCC and institutions like the International Maritime Organization, the International Civil Aviation Organization, the World Trade Organization, or the Montreal Protocol or the Convention on Biological Diversity have not been fully synergistic.

But it should be noted that fragmentation is not necessarily prejudicial. What matters is the effectiveness of the policy response, and in the past it seems relatively clear that the lack of better coordination has hindered the policy response. Regarding its relationships with other regimes or policy spaces, the climate regime has proven to be naturally closed and loosely interacting. Indeed, Parties has been quite indifferent, or even hermetic to what occured elsewhere, regarding the consequences of their action or inaction on other environmental regimes and initiatives, as well as the consequences on other regimes and initiatives on their action within the climate regime. Despite the openness of the 'constitutional' framework, the later has in general functioned in a kind of "clinical isolation"14 from other parts of international law. For example, measures adopted to implement the UNFCCC and its Kyoto Protocol have shown that Parties have had so far little consideration of biodiversity conservation issues, with some very few exceptions in relation to forest and land use management, but always as ancillary consequences of climate mitigation or adaptation objectives. 15 International climate change governance consists of a 'regime complex' rather than just a single regime16 of norms and institutions under the 1992 UN Climate Change Convention, the Kyoto Protocol and now the Paris Agreement. Raustiala and Victor identified a regime complex as "an array of partially overlapping and non-hierarchical institutions governing a particular issue-area". 17 The figure 1 bellow is adapted from the one that Kehoane and Victor proposed of the international regime complex for climate change. As well as the UNFCCC, the complex includes numerous public and private institutions and initiatives which operate at the international, regional, bilateral, national and even subnational level, each with its own focus (for example, expertise with the IPCC, finance, technology, business…) and involving varying levels of commitment. The interactions between these different spheres vary both in their strength, and in whether they are intended or accidental. Orsini, Morin and Young later gave regime complexes the more precise, practical and operational meaning of "a network of three or more international regimes that relate to a common subject matter; exhibit overlapping membership; and generate substantive, normative, or operative interactions recognized as potentially problematic whether or not they are essential in identifying regime complexes and analyzing their effects". 18 After years of an abundant scholarship on the fragmentation of international law, this concept of regime complex has the advantage of highlighting that which links the different regimes together as much as that which divides them. Hence it offers an interesting analytical framework for understanding accurately a complex reality by focusing on the flow of both norms and actors which exist between the different legal and institutional realms. It therefore takes us further forward than the simple, well-established and relatively unhelpful observation that regime fragmentation exists, and towards a greater understanding of the relationships and interactions between these regimes.

From this perspective, we propose to view the Paris Accord as the bedrock of the regime complex for climate change. Otherwise the Accord and the whole regime complex are likely to be ineffective. To this end, the Accord should aim to fulfil two different but complementary objectives:

-on the one hand, a catalysing role to create a dynamic and contribute to raising the level of ambition in the other regimes that form part of the regime complex ;

-on the other hand, to play the leading role in order to orchestrate climate governance, to strengthen coherence and ensure complementarity, ensure work is covered correctly and avoid duplication of effort etc.

The Paris Agreement as the bedrock of the 'regime complex' on climate change

The COP Decision 1/CP.21, adopting the Paris Agreement at COP21, provides for several indicators towards a greater openness to external challenges than in the past. They acknowledge the need for a global approach to such challenges, which goes beyond the forum of meetings of Contracting Parties to the Paris Agreement, the climate COPs. Depending on subjects, bridges have been built in two directions: either the Agreement takes into consideration other objectives or requirements, or it invites Parties or intergovernmental organisations to integrate better the climate change dimension. In its preamble, the Agreement refers to the need to ensure "the integrity of all ecosystems, including oceans, and the protection of biodiversity, recognized by some cultures as Mother Earth", while recognizing the importance of "the conservation and enhancement, as appropriate, of sinks and reservoirs of the greenhouse gases referred to in the Convention".

Regarding forests and sinks, it underlines "the importance of incentivizing, as appropriate, non-carbon benefits associated with such approaches" (art. 5). Such references could improve the coverage of biodiversity protection in the climate change framework which has been so far rather hermetic in that respect.

The preamble of the COP Decision 1/CP.21 also makes a reference to the Sustainable Development Goals, in particular to the SDG 13 on climate change as well as to Addis-Abeba Action Agenda adopted at the United Nations Third International Conference on Financing for Development and even to the Sendei Framework for Disaster Risk Reduction. Indeed, it is crucial to create greater consistency among these global objectives at the international level. The reference to such "meta-norms" could play a key role in strengthening the regime complex on international climate change and linking efforts under the UNFCCC with others in the international environmental and development law arena. It assists in linking the work under the Convention with relevant regimes, environmental and other, to the benefit of each of those regimes. Crucially, it will guide Parties' in their implementation of the Paris Accord so that it is consistent with those other regimes, thus enhancing international legal coherence and reducing fragmentation. The synergistic role of the Aichi Targets in the field of biodiversity protection has already been pointed out. 19 Developing commonalities between regimes through common principles or strategic objectives could help to prevent conflict between multilateral environmental agreements.

A link is also established between climate change and human rights, not in the operative part of the Agreement as initially proposed by some Parties, but in the preamble of the Accord, which emphasizes that "climate change is a common concern of humankind, Parties should, when taking action to address climate change, respect, promote and consider their respective obligations on human rights, the right to health, the rights of indigenous peoples, local communities, migrants, children, persons with disabilities and people in vulnerable situations and the right to development, as well as gender equality, empowerment of women and intergenerational equity". 20 However, this relates to the respect of "respective obligations" of States (existing or to be adopted in another context) : with such qualifier, some wanted to make sure that the Paris Accord would not create new obligations in this area.

On indigenous people, it must be noted that the Paris Accord also mentions the need to take into account traditional knowledge, knowledge of indigenous peoples and local knowledge systems, with a view to integrating adaptation into relevant policies and actions (art. 7, § 5). Noteworthy that indigenous people have welcomed the recognition of the 19 G. FUTHAZAR. The diffusion of the Strategic Plan for Biodiversity and its Aichi targets within the biodiversity cluster: An illustration of current trends in the global governance of biodiversity and ecosystems. YIEL, Vol. 25, No. 1, pp. 133-166. 2015. 20 We can find a similar formula in the preamble of the Paris Decision.

ambitious objective to pursue efforts to limit temperature increase to 1,5° C as compared to pre-industrial levels in Article 2 of the Paris Agreement. However, stating that climate change is a "common concern of humankind" is not new, in as far as it was already affirmed by the preamble UNFCCC since 1992. On finance, there has also been an effort towards greater consistency: the COP Decision "Invites all relevant United Nations agencies and international, regional and national financial institutions to provide information to Parties through the secretariat on how their development assistance and climate finance programmes incorporate climate-proofing and climate resilience measures" ( § 44). In doing so, the Agreement assumes to become the core framework and a catalyst of the strengthened international cooperation on climate change, in and out the UNFCCC. 21 By contrast, there is no reference made in the Paris Agreement to international trade law or agreements. Initially proposed as an option in the Geneva text, it has been withdrawn and not tabled again in the final rounds of talks before COP21. Therefore, the statu quo should remain, with a relative deference from the international climate regime with regard to international trade law. 22 Having in mind how much international trade law, particularly intellectual property rights, can affect its implementation, the Paris Agreement could have integrated, at least, a clause reflecting upon the mutual supportiveness principle. This principle requires consideration of whether there are areas of conflict given that the Parties are required to interpret and apply the rules emanating from the two different legal regimes in a way that is mutually compatible. It is therefore a principle that enables the different regimes to be linked and coordinated whilst avoiding a hierarchy. According to the International Legal Commission, "The assumption is that conflicts may and should be resolved between the treaty partners as they arise and with a view to mutual accommodation". 23 A reference to mutual supportiveness in the Paris Accord would have been helpful to the world of international business by providing a more balanced approach to the relationship between climate change and business than is currently the case. In terms of its environmental and commercial objectives, the Paris Agreement should not be subservient to international commercial law. More generally, it would have been beneficial to promote the principle of mutual supportiveness in the Paris Accord with a fairly general formulation that takes the mutual supportiveness principle out of its usual application specifically to international trade law.

The Paris Accord could have been inspired by the relatively balanced formulation contained in the Legal principles adopted in 2014 by the International Law Association. Article 10 entitled "Inter-Relationships" is expressed thus:

"1. In order to effectively address climate change and its adverse effects, States shall formulate, elaborate and implement international law relating to climate change in a mutually supportive manner with other relevant international law. 2. States in cooperation with relevant international organizations shall ensure that consideration of climate mitigation and adaptation will be integrated into their law, policies and actions at all relevant levels, as laid out in Article 3.

3. According to Article 8, States shall cooperate with each other to implement the interrelationship principle in all areas of international law, whenever necessary (…)" 24 .

Given that it represents a compromise, mutual supportiveness should have been a politically acceptable option and would have benefited the other areas of international environmental cooperation (in particular on ozone layer protection or biological diversity where there has already been some friction) and also more widely to the trade, investment, law of the sea and human rights domains. The clause proposed by the ILA is particularly interesting because it is balanced in aiming to take into account other areas of law in the drafting and implementation of climate law ( §1), it also provides a principle of integration of climate demands into other policy areas at all relevant levels ( §2) and provides, if necessary, for cooperation on the implementation of the principle of internormativity ( §3). In this way, such a clause could enable secondary legislation (for example, previous COP decisions relating to the Paris Accord) to guide the implementation of the Accord in a direction which takes account of other normative areas in an evolutionary way. Such a clause could also inspire other normative areas to take better account of the relevant targets in the Paris Accord in a spirit of "win-win".

To take the example of biodiversity, procedures and modalities for "Intended Nationaly Determined Contributions" 25 implementation could be used to authorise the COP to recommend to Parties that they take into account the need to protect biodiversity, with reference to decisions under the Convention on Biological Diversity (CBD) that relate to certain objectives, means or indicators. Combined with the principle of "no backsliding", such an initiative could produce a domino effect on biodiversity conversation (whose positive effects on climate change mitigation and adaptation are already well-known). Clearly, the level of resistance that can be expected from some Parties to such an initiative should not be under-estimated. This resistance originates from a fear that discussions within the CBD could be "contaminated" through the "importation" of difficulties and structural issues from the UNFCCC. It also stems from a fear of losing sovereignty by "importing" concepts and rules that emanate from the UNFCCC, also remembering that some important Parties such as the US are not parties to the CBD. It may also be worth thinking about the need for better coordinated action with the Montreal Protocol for example on the elimination of HFCs. This shows particularly well the need of coordination between two international regimes, in that case the climate regime and the ozone regime. The increasing use of HFCs is a climate issue, complicated by the international policy aiming to protect the ozone layer. It is exactly at the interface of the two regimes. There is not a single word on that in the Paris Agreement. The issue has been given only marginal consideration on the road to Paris, as an opportunity to mitigate climate change. However, the Paris Agreement created the momentum which has favoured the adoption of an agreement during the Kigali Meeting of the Parties to the Montreal Protocol, in October 201626 . The Kigali amendment will guarantee a better consistency of internation action in favour of climate and ozone.

By promoting voluntary cooperative approaches in its Article 6, the Paris Agreement offers also multiple benefits, both by enhancing the implementation of the climate and other international regimes, and by inspiring and providing good examples to other Parties which could in turn result in an acceleration of the global effort under the Convention. Given the difficulty in making substantial progress involving all Parties, enhanced cooperative action could be a key way of enhancing not just the implementation of work under the Convention, but also under other regimes by promoting synergies with the Convention, and thus reducing fragmentation in the realm of international law.

Conclusion

In recent years, other important environmental issues as forests, biodiversity, ozone, marine acidification, and so on, have in most cases been overshadowed by the issue of human-induced climate change, yet both are equally important, if not fundamental to the ongoing future of human populations and even planetary life. Indeed planetary boundaries are closely connected and this should be duly reflected in policies and legal tools [START_REF] Biermann | Planetary boundaries and earth system governance: exploring the links[END_REF] . As shown by the lack of cross-reference in decisions taken in the context of the international climate change regime, the UNFCCC behaved sometimes like an autistic convention hermetic to external concerns. According to some authors, "the connection with issues other than its own has been seen as an unwanted distraction to achieving its narrowly defined and interpreted object and purpose". [START_REF] Chambers | Interlinkages and the Effectiveness of Multilateral Environmental Agreements[END_REF] COP21 has provided an unic opportunity to make a decisive step toward a better open approach of other issues and regimes. The Paris Agreement shows timid progress from this point of view and States have now to assume their responsibilities. Who can claim today in good faith that the international climate regime could solve on its own the issue of climate change? Indeed the natural fragmentation of international law allows States to instrumentalize one policy space against another in order to protect their domestic interests, thereby undermining overall effectiveness in the end. [START_REF] Doelle | Re-thinking the Role of the UN Climate Regime[END_REF] Here, the "schism of reality" that Amy Dahan and Stefan Aykut pointed out, seems particularly relevant and is problematic. It is the result of a growing gap between a given reality of the world based on the globalization of markets and the overexploitation of fossil fuels, with States being prisoners of a fierce competition who hang on as ever their national sovereignty on the one hand and a negotiating forum supported by international governance arrangements which gives the impression it can be a central regulator being capable of allocating emission rights, but with less and less grip on this given reality. [START_REF] Dahan Dalmedico | Gouverner le climat, 20 ans de négociations internationales[END_REF] Scholars have definitely to pay more attention for the coming years both to interplays between the international regimes 31 but also to the management of regime complexity at the national level. [START_REF] Velázquez Gomar | Regime Complexes and National Policy Coherence: Experiences in the Biodiversity Cluster[END_REF]

FIGURE 1 :

 1 FIGURE 1 : Adapted from The regime complex for managing climate change, R. O. Keohane and D. G. Victor, « The regime complex for climate change », Perspectives on Politics, 2011, vol. 9, pp. 7-23.

  18 A. ORSINI, J.-F. MORIN, O. YOUNG. Regime complexes: A buzz, a boom, or a boost for global governance?, Global Governance: A Review ofMultilateralism and International Organizations, vol.19(1), p. 29. 2013.

  . FCCC/CP/2016/2 , May 2016 ; W. STEFFEN et al. Planetary Boundaries: Guiding human development on a changing planet, Science , Vol. 347, Issue 6223, p. 1. 13 Feb 2015.

	7	See	UNEP,	The	Emissions	Gap	Report	2015,	Summary	for	Policymakers,

http://uneplive.unep.org/media/docs/theme/13/EGR2015ESEnglishEmbargoed.pdf, 8 Synthesis report on the aggregate effect of the intended nationally determined contributions, Note by the secretariat, FCCC/CP/2015/7, 30 October 2015, 66 p. The Paris Decision takes note thereof ( §16). 9 UNEP, UNFCCC Secretariat, Aggregate effect of the intended nationally determined contributions: an update, Synthesis report by the secretariat,

  21 See F. W. ABBOTT, P. GENSCHEL, S. SNIDAL ET B. ZANGL. International Organizations as Orchestrators, Cambridge: Cambridge University Press, 2015. Report of the Study Group of the International Law Commission Finalized by Martti Koskenniemi, A/CN.4/L.682, 13 April 2006, §276.

22

See MALJEAN-DUBOIS Sandrine, WEMAËRE Matthieu. L'accord à conclure à Paris en décembre 2015: une opportunité pour 'dé'fragmenter la gouvernance internationale du climat ? Revue juridique de l

'environnement, 4, p. 657. 2015.

23 ICD, Fragmentation of International Law : Difficulties arising from the Diversification and Expansion of International Law,

UNFCCC, Decision 1/CP.20 (2014), Lima call for climate action.

ICD, Fragmentation of International Law : Difficulties arising from the Diversification and Expansion of International Law, Report of the Study Group of the International Law Commission, A/CN.4/L.702, UNO. 28 July 2006.

CHURCHILL Robin R., ULFSTEIN Geir. Autonomous Institutional arrangements in multilateral environmental agreements : a little notice phenomenom, American Journal of InternationalLaw, October, p. 623. 2000.

ICD, Fragmentation of International Law : Difficulties arising from the Diversification and Expansion of International Law, Report of the Study Group of the International Law Commission Finalized by Martti Koskenniemi, A/CN.4/L.682, § 486. 13 April 2006.

WTO Appelate Body Report, United States -Standards for Reformulated and Conventional Gasoline, WT/DS2/AB/R,29.04.1996, p. 19.

MALJEAN-DUBOIS Sandrine, WEMAËRE Matthieu. Climate Change and Biodiversity. In : Encyclopedia of Environmental Law -Biodiversity and Nature Protection Law, Edward Elgar Publishing, ed. Jona Razzaque et Elisa Morgera, 2016. pp. 295-308.

On regimes, KRASNER S. Structural causes and regime consequences: regimes as intervening variables, InternationalOrganization, vol. 36, n°2, pp. 1-21. 1982.

RAUSTIALA K., VICTOR D. The regime complex for plant genetic ressources, InternationalOrganization, vol. 58, pp. 277-309. 2004.

ILA, Legal Principles Relating to Climate Change Draft Articles (2014), http://www.ilahq.org/en/committees/index.cfm/cid/1029.

 25 UNFCC, Decision 1/CP.19 (2013), Further advancing the Durban Platform.

See http://www.unep.org/africa/news/kigali-amendment-montreal-protocol-another-global-commitment-stopclimate-change.

Acknowledgements. This work has been funded by the Agence nationale pour la recherche française within the project CIRCULEX <ANR-12-GLOB-0001-03 CIRCULEX> and by the Iddri (Paris). The authors would like to warmly thank Thomas Spencer, from the Iddri, for his advice and encouragements and Pierre Mazzega, GET Géosciences Environnement Toulouse UMR5563, CNRS / IRD / Université de Toulouse, for his useful insights and comments.

5.