The propagation of continental shelf waves

Abstract

Taking the case of a continental shelf of exponential slope, and assuming zero horizontal divergence, the authors derive a simple theory of free shelf waves, which, however, is more general than previous theories in that shorter as well as longer waves (in comparison with previous work) are taken into account. The properties of the waves are discussed, and the dispersion curves for each mode are obtained. Although the phase velocities of shelf waves are always in the same sense as those of Kelvin waves, there is a negative group velocity for a range of wavelengths, indicating that energy can propagate in the opposite sense. A similar approach is used to derive a theory for free waves propagating on a shelf between two regions of constant depth. The limiting case of a shelf of zero width is also considered, and is compared with a limiting case of the ‘double-Kelvin’ waves discovered by Longuet-Higgins (1967).