Coastal Kelvin waves in the presence of a slowly varying topography

Abstract

The evolution equation is derived for a weakly nonlinear coastal Kelvin wave propagating in slowly varying topography in anf-plane ocean. For weak transverse variations in the topography, the wave evolution is governed by a perturbed Korteweg–de Vries equation. In the absence of transverse variation, wave dispersion vanishes and the evolution equation reduces to a nonlinear advection equation with variable coefficients. As a general property of these equations, the total mass flux associated with the Kelvin wave is not conserved; residual mass must be generated. It is shown by an asymptotic analysis that this residual mass field is in balance with a mean geostrophic current long after the passage of the Kelvin wave. This result is verified using a numerical model. The physical mechanism evolved in the generation of the residual mass can be understood in terms of potential vorticity conservation.