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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 DrossartLESIA
Collaboration
Proponents :• André Mangeney • Olivier Talagrand (LMD)• Pierre DrossartPhD Students : E. Brottier, A. Abouelainine, V. LesueurExternal 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 presentQuestion: 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
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, = vorticityCharacteristic numbers :
T = Taylor, Coriolis vs viscosityP = Prandtl , ratio of diffusivitiesF = 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 mostunstable spherical harmonics
Non linear calculation
Radial velocity field for E=5 = 10-3
Azimutal velocity on the outer planet E=1.8 =5 x 10-3
Radial velocity for a « Neptune » case E=2.61 =10-4
First results (2)
• Viscous regime
Towards a turbulent 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