Steady currents induced by oscillations round islands

Abstract

An oscillating current such as a tidal stream or an inertial oscillation may have a horizontal scale of the order of many times the local depth of water. Thus an island projecting from an otherwise uniform sea bed will give rise to a local, periodic disturbance near the island. It is shown that this disturbance may be resolved into two waves travelling in opposite senses round the island. If the particle orbits at large distances are circular, then only one of these waves has non-zero amplitude.In addition to the oscillatory motion, however, there is a steady d.c. streaming, or mass-transport velocity, whose magnitude is of order u²/σa where u denotes the magnitude of the oscillatory velocity at large distances, σ denotes the radian frequency, and a is the radius of the island. In this paper the profile of the streaming velocity is calculated for circular islands, with or without shoaling regions offshore. It is shown that resonance with the free modes trapped by the shoaling regions may greatly increase the streaming velocity. Viscosity (or horizontal mixing) also tends to increase the streaming velocity close to the shoreline.The conclusions are supported by some simple model experiments. It is suggested that such streaming may partly account for the observed pattern of currents near Bermuda.