Studies On Convective Stability And Nonlinear Characteristics In Planetary Interior

The rapid development of the space exploration makes planet dynamics become one of the most active research field. Understanding planet dynamics is very important for the astrophysics and geophysics. We know that dynamics process is associated with the celestial bodies mass. The heavier the celestial bodies, the stronger nonlinear dynamics process. Jupiter is the most largest planet, so we select Jupiter as our object to study characteristics in planetary interior convection.We choose an annular rotating about, vertical axis as a model. It is uniformly heated from below, and the temperature below is higher than above. The configuration of a rotating annular channel heated from below can be readily realized in laboratory experiments. Our model with the gravity vector perpendicular to the axis of rotation can mimic the equatorial region of a rotating spherical shell.Based on the model,our work is summarized as follows:(1)We identify three different types of convection in a Boussinesq fluid in our rapidly rotating model(τ ≥ O(10~3)):global oscillatory, wall-localized oscillatory and global stationary convection.(2)The weakly nonlinear problem describing differential rotation and meridional circulation is examined, showing that geostrophic multiple-peaked (two pro-grade and retrograde) differential rotation can be maintained by the Reynolds stresses in wall- localized convective eddies in a rapidly rotating channel.(3)We have derived the first asymptotic solutions of second order accuracy that take account of the velocity boundary conditions imposed on the sidewalls for the boundary-layer convection.(4)We check up the 3D parallel solver-NaSt3DGP accurate, and find out its excellence and disadvantage.(5) We have focused our numerical simulations on narrow and wide different cases in a wide range of the Rayleigh number R; and revealed that, the wall-...