Computation of Thermodynamic and Hydrodynamic Properties of the Viscous Atmospheric Motion on the Rotating Earth in 2D Using Naiver-Stokes Dynamics

Abstract: In this article, we model Earth's lower small-scale eddies motion in the atmosphere as a compressible neutral fluid flow on a rotating sphere. To justify the model, we carried out a numerical computation of the thermodynamic and hydrodynamic properties of the viscous atmospheric motion in two dimensions using Naiver-Stokes dynamics, conservation of atmospheric energy, and continuity equation. The dynamics of the atmosphere, governed by a partial differential equation without any approximation , and without considering latitude-dependent acceleration due to gravity. The numerical solution for those governed equations was solved by applying the finite difference method with applying some sort of horizontal air mass density as a perturbation to the atmosphere at a longitude of $5\Delta\lambda$ . Based on this initial boundary condition with taking temperature-dependent transport coefficient into account, we obtain the propagation for each atmospheric parameter and presented it graphically as a function of geometrically position and time. All of the parameters oscillating with respect to time and satisfy the characteristics of an atmospheric waves. Finally, the effect of the Coriolis force on resultant velocity was also discussed by plotting contour lines for the resultant velocity for the different magnitude of Coriolis force, then we also obtain an interesting wave phenomena for the respective rotation of the Coriolis force. ~~~~Keywords: Naiver-Stokes Equations; Finite difference method; Viscous atmospheric motion; Viscous dissipation; convective motion.