A note on deep Kelvin waves and their propagation through a shear Flow.

Abstract

Current laboratory experiments on topographic effects in rotating non-homogeneous fluids pose certain theoretical questions concerning the properties of waves in a deep rotating stratified fluid. The governing equations admit one class of solutions corresponding to "inertia-gravity waves", which occupy the whole fluid, and another to "Kelvin waves", which arc more localized. Characteristic properties of Kelvin waves arc (a) linear and co-planar trajectories of individual fluid elements, with no motion in one horizontal direction, (b) sense of phase propagation dependent inter alia on the sign of the Coriolis parameter f, (c) speed of phase propagation independent of f and (d) amplitude decaying exponentially in the direction of no horizontal motion at a rate proportional to f. "Deep Kelvin waves" correspond to the case when the horizontal wavenumber is not small compared with the vertical wavenumber. The "critical level" below which Kelvin waves in a shear flow will be largely confined is located where the intrinsic frequency of the wave (i.e. the Doppler frequency relative to the local flow) is equal to zero, as for ordinary gravity waves unaffected by rotation, and not where the intrinsic frequency is equal to ± f which is the case for inertia-gravity waves.