Numerical simulation of downslope flows in a confined stratified region

Geophysical fluids such as atmosphere and ocean often have stable density stratification; hence internal gravity waves are generated and propagated through them which are important in momentum and energy transfer in these media. These waves are also believed to generate layered structures in such media.
Recently there have been numerous theoretical, experimental and numerical studies on the ways that these waves are produced and propagated, including the nature of these internal gravity waves. Density driven flows such as katabatic winds or cold air that flow over the mountain slopes, in stable atmospheric surface layer at night, and the movement of salty dense water over the sloped ocean bottom are examples of mechanisms associated with the generation of internal gravity waves that lead to energy transfer in these stratified regions with various vertical density stratifications.
In the present work, a two dimensional fully nonlinear numerical model is developed for the simulation of a down slope flow in a confined stratified region. The governing equations are written in terms of vorticity and density as prognostic variables, and stream function as a diagnostic variable. A three level leapfrog time stepping method is used to advance the equations in time and a second-order centered finite difference scheme is applied for the spatial differencing of the governing equations.
Numerical results are presented for the way that non-hydrostatic internal gravity waves are generated and propagated as a result of downslope flow in stratified confined region. In addition, numerical results are compared with some existing experimental observations. The results show that the shear layers in the stratified region is produced by the internal waves propagation.
Typical vertical structures in the flow field and the number of layers in the stratified region are similar to that of experimental work. For example the number of layers due to the modal structure of propagating internal gravity waves is 6-7. The normal modes of such internal gravity waves, propagating vertically in stratified regions produce shear layers that may be responsible for layered structures in geophysical flows in nature.