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

Abstract

We model Earth's lower atmosphere as both incompressible and compressible neutral fluid in motion on a rotating sphere and the viscosity of the fluid depends on the density of the air. To justify the model, we carried out a numerical computation of the thermodynamic and hydrodynamic properties of the viscous atmospheric motion in two dimensions at some altitude using Naiver-Stokes dynamics. To interpret the dynamics of a fluid, we considered the governed partial differential equation (PDE) without any approximation then we applied some sort of wind velocity, air mass density, and temperature perturbation to the atmosphere at the boundary position x = 0 using the finite difference method implemented in FORTRAN programing language. The resulting dynamics of the atmosphere are governed by the competition among the various dominant forces, namely, the viscous dissipation, the convective motion, pressure gradient force, centripetal force, and Coriolis force. We numerically obtain the resultant velocity field for Naiver-Stokes equation at a different time taken of simulation by changing the magnitude of the Coriolis force. In addition to this, we consider the first law of the thermodynamics applied to our model. The numerical results show that the temperature, pressure, air mass density, and wind velocity variation with longitude, latitude, and time in the atmospheric fluid due to viscous dissipation, convective motion, work done by pressure gradient force, and the bulk motion of the atmospheric fluid.