New Mathematical Tractates about Dynamics of Great Red Spot on the Jupiter

Abstract

. In the present paper, the mathematical description of the dynamic processes of GRS on Jupiter is carried out. Wherein, at first, an overview and introduction of the main observations of GRS are given and comparison with different studies of other authors. In the present work, theoretical justifications are also presented in order to describe the dynamics of the GRS and its internal structure, i.e. mathematical description of the motion process and rotation details for the dynamics of the GRS on Jupiter. In the present work on the theory of hydrodynamics and gas dynamics, equations of motion of the GRS on Jupiter are obtained, despite the very small applying of hydrodynamics and gas dynamics theories in the dynamic aspect. It should be noted that near the center of the GRS the matter has a viscosity, and the incompressibility conditions are satisfied, the equations in motion related to viscosity, terms pass from the laminar flow to turbulent one, and in these regimes, the problem of dynamics for the GRS is described by using partial differential equations. For the first time, the theory of hydrodynamics in a non-classical approach is applied in order to investigate the dynamics for the GRS on Jupiter, for the global motion of fluid and gas of which, in turn, this compound motion is described by using partial derivative equations. Wherein, the main difficulties were overcome with the help of a non-classical approach, namely flows from laminar (in this case, the peculiarities of new flows, the so-called quasi-laminar, are the main approach in non-classical method) a transient flow (ovals are attached for a turbulent flow) to turbulent motion. It is found that these three compound flows are determined the global dynamics of the GRS on Jupiter. In order to apply the theory of hydrodynamics in the non-classical approach, the theory of a fixed point with parameters  (epsilon) is additionally selected to restore the fulfillment of the conditions: vortices, incompressibility of the fluid, rotation of the elementary volume of the fluid, as well as for turbulence and atmospheric waves. The considered results of such a mathematical approach for the dynamics of the GRS on Jupiter were checked and reliably justified with all the details. Within the proposed mathematical interpretation is justified several observed data obtained by spacecraft, also the results of ground-based observations.