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