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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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pierre drossart lesia

Convection dans les coquilles sphériques et circulation des planètes géantesConvection in spherical shells and general circulation of giant planets

Pierre Drossart



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
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
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
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
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
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
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
First results (1)
  • Threshold for convective instability for various boundary conditions (free, fixed, etc.)

=> Exact comparison possible with Chandrasekhar calculations

first results 2
First results (2)
  • Viscous regime
what have we learned from this program
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
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
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