This study examines the perturbation effect of temperature and density of moist air on atmospheric variables at $9^{o}1^{'}48^{"}$N, $38^{o}44^{'}24^{"}$E and 6.324km above the Earth's surface. The atmosphere is a compressible neutral moist air flowing on a rotating Earth as a model and it's basic atmospheric parameters such as gas constant, transport coefficients, mixing ratio and specific heat capacities are considered to be temperature dependent and the earth's gravity changes with latitude and altitude. To describe the dynamics, we carried out a numerical computation using finite difference method on an unstaggered grid. Our results revealed that the response of all the variables have a plane wave pattern, in which specific heat capacities (SHCs), resultant wind speed (RWS) and water vapor mixing ratio (MR) increase with time at each latitude but vertical wind speed (VWS), specific enthalpy (SE) and pressure decrease with time at each latitude. The increase of MR with time is the result of water vapor flux into the air parcel and the decrease of SE and increase of RWS with time is the result of thermal energy to mechanical energy transformation. The decrease of VWS with time is the effect of the viscous force due to temperature dependence of viscosity.

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.