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In this article, we model Earth's lower small-scale eddies motion in theatmosphere as a compressible neutral fluid flow on a rotating sphere. Tojustify the model, we carried out a numerical computation of the thermodynamicand hydrodynamic properties of the viscous atmospheric motion in two dimensionsusing Naiver-Stokes dynamics, conservation of atmospheric energy, andcontinuity equation. The dynamics of the atmosphere, governed by a partialdifferential equation without any approximation , and without consideringlatitude-dependent acceleration due to gravity. The numerical solution forthose governed equations was solved by applying the finite difference methodwith applying some sort of horizontal air mass density as a perturbation to theatmosphere at a longitude of $5\Delta\lambda$ . Based on this initial boundarycondition with taking temperature-dependent transport coefficient into account,we obtain the propagation for each atmospheric parameter and presented itgraphically as a function of geometrically position and time. All of theparameters oscillating with respect to time and satisfy the characteristics ofan atmospheric waves.  Finally, the effect of the Coriolis force on resultant velocity was alsodiscussed by plotting contour lines for the resultant velocity for thedifferent magnitude of Coriolis force, then we also obtain an interesting wavephenomena for the respective rotation of the Coriolis force.  ~~~~Keywords: Naiver-Stokes Equations; Finite difference method; Viscousatmospheric motion; Viscous dissipation; convective motion.

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