1. Convection dans les coquilles sphériques et circulation des planètes géantes Convection in spherical shells and general circulation of giant planets Pierre Drossart LESIA

2. Collaboration Proponents : André Mangeney Olivier Talagrand (LMD) Pierre Drossart PhD Students : E. Brottier, A. Abouelainine, V. Lesueur External collaborations : M. Rieutord, M. Faure, J.I. Yano, … Time scale : 1986-1996

3. Situation of the question Giant planets: -global radiative balance > solar heating -General circulation = zonal -Alternance of bands with +/- zonal velocities -Small pole-equator temperature gradient

4. Giant planets meteorology: -banded structure -Highly turbulent regime -Internal heating source

5. Internal heating Source : separation of He in the internal core or residual contraction (?) => internal convection present Question: is the general circulation and the banded appearance due to solar heating OR internal heating ? Dimensionless parameter : E = ratio of emitted to solar heating  ratio of conductive time to radiative time

7. Numerical simulation (new approach in the context of the mid-80’s…) Full spherical (spherical shell) approach 3D simulation Approximation for convection : Boussinesq (neglecting compressibility effects, except for thermal dilatation)

8. General adimensional Equations …………………. Fields : u = velocity, P = pressure, T = temperature,  = vorticity Characteristic numbers : T = Taylor, Coriolis vs viscosity P = Prandtl, ratio of diffusivities F = Froude, centrifugal force vs gravity

11. Boundary conditions Rigid or free conditions at the inner and outer shells Temperature conditions adapted to the planetary conditions Pressure condition : Kleiser- Schumann method for ensuring exact conditions at the boundary Thermal conditions related to observed planetary conditions

14. Numerical approach Spectral methods Semi-implicit scheme Chebyshev spectral decomposition for the fields (FFT related) Exact boundary conditions – adapted to planetary conditions Computers : CONVEX (Observatoire), Cray (CIRCE/IDRISS), …

15. First results (1) Threshold for convective instability for various boundary conditions (free, fixed, etc.) => Exact comparison possible with Chandrasekhar calculations

16. Linear solution : convective instability for the most unstable spherical harmonics

17. Non linear calculation

18. Radial velocity field for E=5  = 10 -3

19. Azimutal velocity on the outer planet E=1.8  =5 x 10 -3

20. Radial velocity for a « Neptune » case E=2.61  =10 -4

21. First results (2) Viscous regime

22. Towards a turbulent regime

23. What have we learned from this program Geostrophic solution for deep circulation Deep circulation can be maintained by solar heating at the boundary condition ! Zonal circulation appear at the outer boundary Extension of Hide’s theorem in the deep shell regime Inversion of the zonal circulation compared to geostrophic solution

24. Extension of the science program Collaboration with J.I. Yano : other approaches Collaboration with A. Sanchez-Lavega (Bilbao) for specific topics in Giant Planets dynamics (hot spot dynamics)

25. Conclusions of this work Robust and validated program, method re-used by several other projects Good introduction (for LESIA) in the field of dynamics, Initiation of a fruitful long term collaboration between LESIA and LMD Two PhD thesis Few publication (low bibliometrics, but …) The G.P. Circulation problem is still there ! and …

26. Most important : …. a lot of fun