TITLE:
A New Mathematical Justification for the Hydrodynamic Equilibrium of Jupiter
AUTHORS:
Mahammad A. Nurmammadov
KEYWORDS:
GRS, Jupiter, Cyclones, Anticyclones, Circulation, Rotation
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.12 No.9,
September
26,
2022
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.