A New Mathematical Justification for the Hydrodynamic Equilibrium of Jupiter

Abstract

In this paper, the case of Jupiter being found in hydrodynamic equilibrium is for the first time investigated solely by mathematical methods. With the help of the hydrodynamic method, formulas of energy balance for oval and vortex are found, which are summed as permanent kinetic energy and constantly provide equilibrium for the stable rotational movements of Jupiter. To find the total kinetic energy of the oval and vortex in turbulent mode, Green’s function methods with special definitions and flow functions that describe the movement of the vortex are applied. The results are expressed in lemmas and theorems. For the hydrodynamic equilibrium of Jupiter, the necessary and sufficient conditions for the preservation of the cyclone and the anticyclone are mentioned. The relationships between the angular velocity and the gradient of pressure and the Corolias parameter are also given. The Rossby number is given for steady rotational motion. These facts show the existence of necessary and sufficient conditions for maintaining the stability of rotational motion and prove the hydrodynamic equilibrium of Jupiter. In this case using stream function and constructing generalized Green’s function and accordance energy conservation laws, the hydrodynamic equilibrium of Jupiter is proved.