Waves on the beta-plane over sparse topography

Abstract

This paper deals with linear waves on the beta-plane over topography. The main assumption is that the topography consists of isolated radially symmetric irregularities (random or periodic), such that their characteristic radii are much smaller than the distances between them. This approximation allows one to obtain the dispersion relation for the frequency of wave modes; and in order to examine the properties of those, we consider a particular case where bottom irregularities are cylinders of various heights and radii. It is demonstrated that if all irregularities are of the same height, h, there exist two topographic and one Rossby modes. The frequency of one of the topographic modes is ‘locked’ inside the band (−fh/2H₀, fh/2H₀), where f is the Coriolis parameter and H₀ is the mean depth of the ocean. The frequencies of the other topographic mode and the barotropic Rossby mode are ‘locked’ above and below the band, respectively. It is also demonstrated that if the heights of cylinders are distributed within a certain range, (−h₀, h₀), no harmonic modes exist with frequencies inside the interval (−fh₀/2H₀, fh₀/2H₀). The topographic and Rossby modes are ‘pushed’ out of the ‘prohibited’ band.