On the possibility of Kelvin-type motion in actual seas

Abstract

Amphidromic patterns, characteristic of tidal waves, can be reproduced by a standing Kelvin wave in a rotating basin of constant depth; mathematically a Kelvin wave is represented by a sinusoidal function of a complex variable. Even though such a simple function does the task and can even simulate the distortion induced by bottom friction, it must be recognized that the model sea in which the wave appears is highly simplistic. Consequently we investigate if Kelvin type motion, defined by a null transverse velocity component in the field of currents, can actually be generated in seas of variable bathymetry or on a spherical Earth. In fact the balance between the Coriolis acceleration on the current and the transverse gradient in elevation, a necessary condition for this to occur, can be maintained under any circumstance. To induce Kelvin-type motion in a rectilinear current field is mathematically equivalent to transforming the solution describing the longitudinal variation into a new function having the same form, but dependent on a specific linear combination of the longitudinal and transverse variables. Numerical examples are worked out analytically as well as with the help of computer generation: they confirm the correctness of the mathematics developed. The influence of bottom friction is also illustrated.