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

Mahammad A. Nurmammadov, Adalet Atai
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引用次数: 2

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.
木星大红斑动力学的新数学描述
. 本文对木星上GRS的动态过程进行了数学描述。其中,首先概述和介绍了GRS的主要观测结果,并与其他作者的不同研究进行了比较。在本工作中,还提出了描述GRS动力学及其内部结构的理论依据,即木星上GRS动力学的运动过程和旋转细节的数学描述。在目前的流体力学和气体动力学理论工作中,得到了木星上GRS的运动方程,尽管流体力学和气体动力学理论在动力学方面的应用很少。值得注意的是,在GRS中心附近,物质具有粘性,并且满足不可压缩条件,与粘性有关的运动方程,项由层流变为湍流,在这些状态下,GRS的动力学问题用偏微分方程来描述。本文首次应用非经典流体力学理论研究了木星上GRS的动力学问题,并对其流体和气体的整体运动进行了描述,进而用偏导数方程描述了这种复合运动。其中,主要的困难是在非经典方法的帮助下克服的,即从层流(在这种情况下,新流动的特性,所谓的准层流,是非经典方法的主要方法)到瞬态流动(湍流附加椭圆)到湍流运动的流动。发现这三种复合流决定了木星上GRS的全局动力学。为了将流体力学理论应用于非经典方法中,还选择了参数为(epsilon)的不动点理论来恢复旋涡、流体的不可压缩性、流体的基本体积的旋转以及湍流和大气波等条件的满足。这种数学方法对木星上GRS动力学的考虑结果进行了检查,并以所有细节可靠地证明了这一点。在提出的数学解释中,一些由航天器获得的观测数据以及地面观测的结果是合理的。
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