Theory of waves in the lee of mountains

Abstract

SUMMARYThe disturbance in an air current, whose velocity may vary with height, caused by irregularities in the ground, is obtained. For a wave-like corrugation of the ground of wavelength m / k , small enough for the earth's rotation to be neglected, the stream function of the disturbance satisfiesSome circumstances in which waves may have large amplitude only in the lower layers of the atmosphere are described. In order that such waves may occur over level ground in the lee of mountains the parameter 1 must normally decrease upwards, where With two layers, the lower of depth h, these waves can occur if Fourier's integral theorem is used to obtain the flow in two instances. Fig. 3 shows the wave due to a single long ridge in a stream in which the wind is stronger at higher levels. Fig. 5 shows the flow of a shallow current descending from a plateau, the air being calm above.Nodal surfaces, as in Fig. 5, occur only when the depth of the layer exceeds a critical value, depending on the details of wind speed and temperature.The well-known cloud phenomena associated with the waves are briefly described in section 6, and in section 7 the eRect of isolated mountains rather than long ridges is considered.The theory is only valid for streamline, dry, isentropic, inviscid flow in which the disturbance is only a small proportion of the wind velocity.

Martian atmospheric Lee waves

“…Solving the set (4), (5) and (Ci) under the condition that the wave energy decreases with height, that is the waves are trapped (Corby and Sawyer, 1558;Scorer, 1949), the eigenvalue equation for the wave numbers k is obtained, …”

“…The theory of mountain lee waves has been discussed in a series of papers by Scorer (1949Scorer ( , 1953Scorer ( , 1954, among others, and 0.…”

WRF simulation of downslope wind events in coastal Santa Barbara County

“…The Froude number, defined as the ratio of kinetic energy of the flow to the potential energy required to rise over the mountain (Holton, 2004), can be used to identify when conditions favor the development of mountain waves. Furthermore, the Scorer Parameter, which identifies vertical profiles of wind and stability that reflect vertically propagating wave energy above the mountaintop back to the surface (Scorer, 1949), can be used to identify when mountain waves will generate surface windstorms (e.g. Doyle and Shapiro, 1999).…”

High‐resolution short‐term quantitative precipitation forecasting in mountainous regions using a nested model

“…These influences include forced lifting of air parcels over the terrain, lee waves, convective currents induced by elevated heating of the air surrounding mountain peaks, and the seeder-feeder mechanism by which rainfall from higher clouds scours out cloud droplets from orographically induced cap clouds over terrain peaks [Scorer, 1949;Bergeron, 1960 Though these influences are important, the resolution of operational numerical weather prediction (NWP) models is not yet sufficiently fine to capture these effects explicitly, and current constraints on computing power preclude an immediate solution to this problem. Several approaches have been explored for incorporating finer-scale information into quantitative precipitation forecasts (QPFs) in a more computationally parsimonious manner.…”

“…These influences include forced lifting of air parcels over the terrain, lee waves, convective currents induced by elevated heating of the air surrounding mountain peaks, and the seeder-feeder mechanism by which rainfall from higher clouds scours out cloud droplets from orographically induced cap clouds over terrain peaks [Scorer, 1949;Bergeron, 1960;Hosler et al, 1963;StorebO, 1976;Hill et al, 1981].…”