| A great deal of research concerning phase and group speeds of oceanic planetary waves has taken place since the discovery from satellite altimeter data that such waves are ubiquitous, but travel somewhat faster than predicted by linear theory. Almost all of this research has concentrated on long, i.e. geostrophic, waves for simplicity. In this work we consider the dispersion relation for planetary waves of any wavelength, subject only to the requirement that the wave frequency be small compared with the Coriolis parameter, when the wave is propagating through a mean background flow, varyingstratification, and with a sloping bottom. In most cases, a new wave mode appears for short waves which is essentially non-dispersive, concentrated around some mid-depth value, and is evanescent towards surface and floor. This mode is approximately Doppler-shifted with the local mean flow component along the wavevector. |
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