  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.
