Linear theory of stratified hydrostatic flow past an isolated mountain

Abstract

The stratified hydrostatic flow over a bell-shaped isolated mountain is examined using linear theory. Solutions for various parts of the flow field are obtained using analytical and numerical Fourier analysis. The flow aloft is composed of vertically propagating mountain waves. The maximum amplitude of these waves occurs directly over the mountain but there is also considerable wave energy trailing downstream along the parabolas $y^2=\left(\frac{Nzax}{U}\right)$ Near the ground, the asymmetric pressure field causes the incoming streamlines to split to avoid the mountain and this lateral deflection persists downstream. The horizontal divergence associated with this lateral deflection is balanced by the descent of potentially warmer air from aloft. The relationship of linear theory to other three-dimensional models is discussed. The approach to the two-dimensional infinite ridge limit and non-hydrostatic effects are also discussed.