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Convection dans les coquilles sphériques et circulation des planètes géantes Convection in...
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Transcript of Convection dans les coquilles sphériques et circulation des planètes géantes Convection in...
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