Waves on the beta-plane over sparse topography

This paper deals with linear waves on the beta-plane over topography. The m ain assumption is that the topography consists of isolated radially symmetr ic irregularities (random or periodic), such that their characteristic radi i are much smaller than the distances between them. This approximation allo ws one to obtain the dispersion relation for the frequency of wave modes; a nd in order to examine the properties of those, we consider a particular ca se where bottom irregularities are cylinders of various heights and radii. It is demonstrated that if all irregularities are of the same height, h, th ere exist two topographic and one Rossby modes. The frequency of one of the topographic modes is 'locked' inside the band (-fh/2H(0),fh/2H(0)), where f is the Coriolis parameter and H-0 is the mean depth of the ocean. The fre quencies of the other topographic mode and the barotropic Rossby mode are ' locked' above and below the band, respectively. It is also demonstrated tha t if the heights of cylinders are distributed within a certain range, (-h(0 ), h(0)), no harmonic modes exist with frequencies inside the interval (-fh (0)/2H(0), fh(0)/2H(0)). The topographic and Rossby modes are 'pushed' out of the 'prohibited' band.