The atmosphere is chaotic in nature and full of random processes. This randomrnprocess affects the atmospheric field variables directly or indirectly. In this thesis, tornidentify the effect of random height disturbance, linearized shallow water equation isrnused as a model. The equation is solved numerically using finite difference method onrnnonstaggered Arakwan grid A. When the geopotential height is randomly disturbed,rnthe initial distribution of the velocity field creates a wave of a standing type thatrnconsists of an enhanced and diminished pattern depending on the magnitude of thernperturbation. However in the presence of mean flow, the perturbed system and therninitial distribution of the field variables are carried away based on the direction of thernmean flow