Inertial waves and inertial oscillations in channels

Abstract

A theory is considered for the inertial response of a stratified flat-bottomed channel, with straight walls, to longshore wind. The discussion is focused particularly on transient variables, such as inertial oscillations and waves. The purely “slab-like” inertial oscillations, which occur only in the horizontal currents, are in direct response to the wind. Inertial waves are generated at coastlines and propagate offshore; in the vertical, they have the shape of the associated vertical modes. These waves, which can be expressed by infinite sums of Poincarécross-oscillations, are dispersive with locally varying frequencies and wavenumbers. Close behind the wave fronts, which move at the maximum group velocity of the associated vertical mode, the frequencies and wavenumbers are relatively high. Far behind the fronts, the frequency approaches the local inertial frequency, f, and the wavenumber becomes smaller. Contrary to a semi-infinite ocean, where inertial waves propagate away from a source and decay algebraically, inertial waves in a channel are being reflected at the opposing coastlines and may propagate back and forth. After reflection, their dispersive properties are conserved and the resulting patterns are characterized by locally varying frequencies and wavenumbers. Hence, seemingly stochastic patterns may sometimes occur; therefore, the properties of inertial waves in a channel are quite different from those of a semi-infinite ocean.