Resonant interactions of shelf waves with wind-generated effects

Abstract

Abstract A periodic wind produces an oscillating response when it blows across an ocean overlying a continental shelf. In this paper, the response of a frictionless, horizontally non-divergent ocean to a wind system which travels along the shelf is considered. It is shown that the periodic response produced by such wind systems may have a resonant non-linear interaction with shelf waves whose frequency is close to half that of the wind. The theory may have applications to east-west continental shelves (for example, the south coast of Australia) when strong weather systems move eastward along the shelf. A prerequisite for the onset of resonance is that the travelling wind system may be characterised as a progressive wave whose frequency and wavenumber are close to twice those of any free shelf wave. The growth rate of unstable waves is exponential in time or distance with exponent proportional to the strength of the non-linear interaction. The bandwidth of the unstable wavenumbers and the bandwidth of wavenumbers and frequencies characterising possible resonant wind systems are also proportional to the strength of the interaction.