Anelastic Semigeostrophic Flow Over a Mountain Ridge
Abstract
Scale analysis indicates that five nondimensional parameters (R(0) sq, epsilon, mu, lambda and kappa lambda) characterize the disturbance generated by the steady flow of a uniform wind (U0, V0) incident on a mountain ridge of width alpha in an isothermal, uniformly rotating, uniformly stratified, vertically semi-infinite atmosphere. Here mu = h(0)/H(R) is the ratio of the mountain height h(0) to the deformation depth H(R) = fa/N where f is the Coriolis parameter and N is the static buoyancy frequency. The parameters lambda = H(R)/H and kappa lambda are the ratios of H(R), to the density scale height H and the potential temperature scale height H/R respectively. There are two Rossby numbers: One based on the incident flow that is parallel to the mountain, epsilon = V0/fa, and one normal to the mountain, R(0) = U0/fa. If R(0) sq < 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 mu and epsilon tend to zero. If the flow is Boussinesq (lambda = 0), then the semigeostrophic solutions expressed in a streamfunction coordinate can be derived from the quasi-geostrophic solutions in a geometric height coordinate. If the flow is anelastic (lambda = 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1987
- Accession Number
- ADA480459
Entities
People
- Pe-cheng Chu
- Peter R. Bannon
Organizations
- Pennsylvania State University