FINITE-AMPLITUDE MOUNTAIN WAVES IN A COMPRESSIBLE ATMOSPHERE INCLUDING THE EFFECTS OF DISSIPATION

Adiabatic, two-dimensional, steady-state finite-amplitude, hydrostatic gravity waves produced by flow over a ridge are considered. Nonlinear self advection steepens the wave until the streamlines attain a vertical slope at a critical height zc. The height zc, where this occurs, depends on the ridge crest height and adiabatic expansion of the atmosphere. Dissipation is introduced in order to balance nonlinear self advection, and to maintain a marginal state above zc. The approach is to assume that the wave is inviscid except in a thin layer, small compared to a vertical wavelength, where dissipation cannot be neglected. The solutions in each region are matched to obtain a continuous solution for the streamline displacement δ. Solutions are presented for different values of the nondimensional dissipation parameter β. Eddy viscosity coefficients and the thickness of the dissipative layer are expressed as functions of β, and their magnitudes are compared to other theoretical evaluations and to values inferred from radar measurements of the stratosphere. The Fourier spectrum of the solution for zzc is shown to decay exponentially at large vertical wave numbers n. In comparison, a spectral decay law n-8/3 characterizes the marginal state of the wave at z = zc. © 1990 Gordon and Breach, Sciena Publishers. Inc.