Anelastic semigeostrophic flow over a mountain ridge

Scale analysis indicates that five nondimensional parameters (R₀ ², 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. Here μ = h₀/H_R is the ratio of the mountain height h₀ to the deformation depth H_R = fa/N where f is the Coriolis parameter and N is the static buoyancy frequency. The parameters λ = H_R/H and kλ are the ratios of H_R to the density scale height H and the potential temperature scale height H/k respectively. There are two Rossby numbers; ε = V₀/fa, and R₀ = U₀/fa. If R₀ ² ≤ 1, then the mountain-parallel flow is in approximate geostrophic balance and the flow is semigeostrophic. If the flow is anelastic (λ ≃ 1), no direct correspondence between the two approximations was found. However the anelastic effects are qualitatively similar for the two and lead to: i) an increase in the strength of the mountain anticyclone, ii) a reduction in the extent (and possible elimination) of the zone of blocked, cyclonic flow, iii) a permanent turning of the flow proportional to the mass of air displaced by the mountain, and iv) an increase in the ageostrophic cross-mountain flow. The last result implies an earlier breakdown of semigeostrophic theory for anelastic flow over topography. Apart from a strengthening of the cold potential temperature anomaly over the mountain, the presence of a finite potential temperature scale height (ie k nonzero) does not significantly alter the flow solution. -from Authors