Gravitational and Geostrophic Billows: Some Exact Solutions

Abstract

Gerstner's exact solution for surface waves can be modified to describe waves on an interface between two fluids or air masses, one fluid moving as described by the kinematics of Gerstner waves, the other fluid in wave-trapped uniform motion moving at the speed of the waves, at least in the region between crest and trough. For gravity billows the waves obey the dispersion of the internal waves on a discrete density interface. For geostrophic flow, one obtains frontal waves. Both wave fields are of finite amplitude and constitute exact, although somewhat artificial, solutions.