Studies On Convection Instability And Differential Rotation In Planetary Interior

The rapid development of space exploration makes planet dynamics become oneof the most active research fields. Understanding the dynamics of the planets is veryimportant for the astrophysics and geophysics. People want to know more detailprocess of the birth of the magnetic field, the dynamics of the fluid core and theatmosphere, so we can know the evolution of the solar system. In this paper we aimedat the convection and the different rotation in the planetary interior.Our works summarized as follows are based on the quasi-greostrophysicapproximation model:1. We model a rapidly rotating stellar convection zone by a large-gap sphericalannulus using a two-dimensional quasi-geostrophic approximation incorporating fullspherical geometry and the equation of mass conservation. It is demonstrated that theprimary features of thermal instabilities in rapidly rotating spheres or sphere shells arequantitatively captures by large-gap spherical annuluses using the newquasi-geostrophic approximation.2. Introduced a domain decomposition method suitable the massively parallelcomputers into the numerical simulation. It can help us improving the efficiency ofthe parallel. Investigated the results of numerical simulations of convection forplanetary core, giant planets atmosphere and extra solar synchronized planets. For theweakly nonlinear convection, the results of simulation support the multi-layer-wavestructure first suggested in an analytical model for Jovian atmosphere by Busse(1976).When the nonlinear effect and the corresponding Reynolds stresses becomesufficiently large, the mean flow becomes prevailing: the strongly nonlinear flow, dominated by the spatially regular axisymmetric flow, gains the spatial regularity lostin mildly nonlinear convection.3 Saturation and temporal variation of the mean zonal flow in rapidly rotatingquasi-geostrophic spherical systems are investigated. Convective instabilities generatehighly coherent small-scale eddies which feed energy into the mean flow via theinverse cascade mechanism. We show that this inverse cascade causes a continualpiling up of energy in the mean flow which, in turn, strongly stabilizes the system andhence dramatically reduces the amplitude of the eddies, leading to the reduction andsaturation of the mean flow. This implies that a steady state for the fast equatorialzonal jets on giant planets cannot exist.