Dissipation of linear mountain waves over a ridge

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Stationary vertically propagating mountain waves generated by flow over a bell-shaped ridge are considered. Dissipation by momentum diffusion is introduced when the disturbed isentropes become nearly vertical. Momentum diffusion, characterized by a constant eddy diffusion coefficient, partially suppresses the amplitude growth of the wave that is a consequence of conservation of wave-energy density. The propagating wave can continue to grow in amplitude until neutral static stability is achieved. At higher levels, wave overturning could be expected to occur. The present solution is contrasted with the solution over a sinusoid. In the latter case, wave saturation can occur, whereby a constant wave amplitude can be maintained by a balance between exponential growth and dissipative decay. Wave momentum flux and its divergence, calculated from each type of solution, are compared. The results are relevant to the parameterization of wave drag associated with the vertical propagation of internal gravity waves. It is concluded that parameterization schemes that incorporate wave drag by use of a monochromatic wave response need to be modified to include the presence of a spectrum of waves from realistic wave sources, such as orography. It appears that the required modifications are principally quantitative adjustments to eddy diffusion coefficients, which take account of the fact that a saturation wave-amplitude cannot be attained for a unique value of the diffusion coefficient.DOI: 10.1034/j.1600-0870.1991.t01-2-00005.x
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