On the propagation of ocean waves on a sphere

Abstract

Waves on the ocean are described by means of a directional power spectrum which varies with position and time. This function must satisfy an equation expressing conservation of wave energy. If there is no wave generation or dissipation, the energy equation has a simple olution by which it i possible to work out examples relating wave spectra at different places and times. orne examples of steady tate and initial value problems are presented. Solutions on a sphere and on a plane are compued. The method can be extended to deal with most types of dispersive waves on the surface of a sphere. Generation and di. ipation are expressed by a generating function which expresses the rate of increase of wave energy per unit area for each spectral component. For certain simple forms of this function exact solu tions can be obtained for duration.Jimited and fetch-limited waves. Simple types of wave dissipation can also be treated. If a reasonable generating function can be postulated or derived thoeorically the method should prove useful for rapid automatic wave forecasts.