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Convection dans les coquilles sphériques et circulation des planètes géantes Convection in spherical shells and general circulation of giant planets. Pierre Drossart LESIA. Collaboration. Proponents : André Mangeney Olivier Talagrand (LMD) Pierre Drossart PhD Students :
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Convection dans les coquilles sphériques et circulation des planètes géantesConvection in spherical shells and general circulation of giant planets Pierre Drossart LESIA
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
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
Giant planets meteorology: • banded structure • Highly turbulent regime • Internal heating source
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 e : ratio of conductive time to radiative time
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)
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
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
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), …
First results (1) • Threshold for convective instability for various boundary conditions (free, fixed, etc.) => Exact comparison possible with Chandrasekhar calculations
Linear solution : convective instability for the most unstable spherical harmonics
First results (2) • Viscous regime
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
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)
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 …
Most important : …. a lot of fun