Steady Finite-Amplitude Baroclinic Flow over Long Topography in a Rotating Stratified Atmosphere

Abstract

A steady, inviscid, vertically sheared flow past a large mountain ridge in a rotating stratified atmosphere is considered. The Boussinesq approximation is employed and the flow is bounded above by a horizontal rigid lid. Scale analysis indicates that the flow field is nearly balanced in the vertical and cross-topography directions. The Rossby number need not be small but different scale-analyses are required when the radius of deformation is either large or small compared to the geometrical horizontal scale of the topography. A single equation, expressing the conservation of potential vorticity, determines the pressure field induced by the topography. For a given topography the solution depends on the upstream shear parameter and on the Burger number. The zeroth-order far-field behavior is a function only of the shear parameter and the cross-sectional area of the topography. It is demonstrated that the interaction of topography with a flow which possesses vertical shear upstream leads to the amplification of this shear downstream with a corresponding concentration of isotherms. This may lead to baroclinic instabilities on the lee side of a mountain ridge. Different topographies are considered in the shear-free case and analytical solutions are obtained. It is found that for sufficiently large Burger numbers the topography exerts its influence over horizontal distances which are large compared to its geometric horizontal extent. Furthermore, the first-order far-field behavior depends strongly on the nature of the topography. When the stratification is sufficiently strong the slopes of a mountain ridge may become sites for local Kelvin-Helmholtz instabilities. The analysis indicates that the model remains valid as long as the square root of the Burger number times the geometric characteristics of the topography (height-slope combination) is less than unity. It is conjectured that when this criterion is violated blocking may result and that the flow field would go around rather than over the topography. The scale analysis leads to a simple drag law and a simple formula is obtained for this drag when the topography is symmetrical and the upstream flow possesses no shear.