14 - Wave propagation

Summary

The governing equations support several forms of wave motion. Atmospheric waves are excited when air is disturbed from equilibrium (e.g., mechanically when air is displaced over elevated terrain or thermally when air is heated inside convection). By transferring momentum, wave motions convey the influence of one region to another. This mechanism of interaction enables tropical convection to influence the extratropical circulation. It also enables the troposphere to perturb the stratosphere, driving it out of radiative equilibrium (Fig. 8.27).

DESCRIPTION OF WAVE PROPAGATION

Wave motion is possible in the presence of a positive restoring force. By opposing disturbances from equilibrium, the latter supports local oscillations in field properties. Under stable stratification, buoyancy provides such a restoring force (Sec. 7.3). The compressibility of air provides another. The variation with latitude of the Coriolis force provides yet another restoring force. It will be seen to support large-scale atmospheric disturbances.

Surface water waves

The description of wave motion is illustrated with an example under nonrotating conditions, which will serve as a model of buoyancy oscillations in the atmosphere. Consider disturbances to a layer of incompressible fluid of uniform density ρ and depth H (Fig. 14.1). The layer is bounded below by a rigid surface. It is bounded above by a free surface, namely, one that adjusts position to relieve any stress.