On the airflow over mountains with gentle slopes

The nonlinear equations for the two-dimensional small scale steady-state flow of a compressible fluid are put in a form appropriate for the treatment of streamlines with gentle slopes. For the limiting case when the slopes of the streamlines are negligibly small, these equations are solved numerically and the obtained results compared with the solutions of the linearized equations to determine the limits within which the linearization is permissible. Few numerical examples are given, to demonstrate the difference between solutions obtained by linearized and nonlinearized models of the atmosphere. It was found that the restriction that the total velocity of the wind be positive plays a decisive role in determining the maximum thickness of the air layer which is able to pass over a mountain of certain height.