Anelastic Semigeostrophic Flow over a Mountain Ridge

Abstract

Abstract Scale analysis indicates that five nondimensional parameters (R02 ϵ, μ λ and kλ) characterize the disturbance generated by the steady flow of a uniform wind (U0, V0) incident on a mountain ridge of width a in an isothermal, uniformly rotating, uniformly stratified, vertically semi-infinite atmosphere. Here μ = h0/HR is the ratio of the mountain height h0 to the deformation depth HR = fa/N where f is the Coriolis parameter and N is the static buoyancy frequency. The parameters λ = HR/H and kλ are the ratios of HR to the density scale height H and the potential temperature scale height H/k respectively. There are two Rossby numbers: One based on the incident flow that is parallel to the mountain. ϵ = V0/fa, and one normal to the mountain, R0 = U0/fa. If R02 ≪1, then the mountain-parallel flow is in approximate geostrophic balance and the flow is semigeostrophic. The semigeostrophic case reduces to the quasi-geostrophic one in the limit as μ and ϵ tend to zero. If the flow is Boussinesq (λ = 0), the...