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 Nzax U y* = -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.

Mountain Weather: Observation and Modeling

“…The blocking usually occurs when a low-level stably stratified layer is stopped by the mountain irregularities at the windward side (Barry, 1981;Jiang, 2003;Smith, 1979Smith, , 1980Whiteman, 2000). This results in a developing high-pressure system and that affects the pressure gradient along the approaching synoptic weather system.…”

Building resolving large-eddy simulations and comparison with wind tunnel experiments

“…Elementary stratified flows with uniform ambient wind U 0 and buoyancy frequency N past obstacles of height h are characterized solely by the Froude number, Fr " U 0 /Nh [45]. Of special interest is the fluid regime with Fr [ 0.5, frequently referred to as low-Froude-number or strongly stratified flow.…”

Internal waves generated by a moving sphere and its wake in a stratified fluid

“…Good qualitative agreement was found some distance downstream of the obstacle and outside the wake region (Peat and Stevenson 1975;Makarov and Chashechkin 1981;Chashechkin 1989). Attempts to include in the theory the finite dimension of the moving body have also been made (Long 1955;Crapper 1959;Smith 1980;Gorodtsov and Teodorovich 1982;Janowitz 1984) and a detailed study of the flow structure and the waves in the lee of surface mounted obstacles, representing three-dimensional hills, has also been made by Hunt and Snyder (1980) and Castro et al (1983). The flow structure and wave field of bodies of revolution at low Reynolds number is accessible by numerical simulation as was beautifully demonstrated by Hanazaki (1988) who simulated the flow field of a sphere at Re = 200 moving in a linearly stratified fluid.…”