Currents induced by tides and gravity waves

Abstract

Two-dimensional oscillatory potential flow was shown by Rayleigh and Schlichting to give rise to a steady second-order streaming at the outer edge of a laminar boundary layer. Their method is here extended to a three-dimensional oscillatory flow which may be represented at a plane boundary by two harmonic oscillations (U, V) of frequency s?/2π in perpendicular horizontal directions. The resulting second-order mean velocity components are interpreted in terms of bottom currents induced by tidal motion in shallow seas, or by doubly modulated gravity waves. These currents depend critically on the relative magnitudes of U, V and f/s?, where f is the Coriolis parameter. It is suggested that on the tidal scale, such currents may contribute to the circulation within the North Sea, while on the gravity wave scale they contribute to the formation of offshore sandbars around the coasts.DOI: 10.1111/j.2153-3490.1963.tb01397.x