Resonance and trapping of topographic transient ocean waves generated by a moving atmospheric disturbance

Abstract

Proudman resonance amplifies the oceanic forced wave beneath moving atmospheric pressure disturbances. The amplification varies with water depth; consequently, the forced wave beneath a disturbance crossing topography radiates transient free waves. Transients are shown to magnify the effects of Proudman resonance for disturbances crossing the coast or shelf at particular angles. A Snell like reflection law gives rise to a type of resonance for relatively slow moving disturbances crossing a coast in an otherwise flat-bottomed ocean. This occurs for translation speeds less than the shallow water wave speed for disturbances approaching the coast at a critical angle given by the inverse sine of the Froude number of the disturbance. A disturbance crossing the shelf at particular angles can also excite seiche modes of the shelf via generation of a transient at the continental slope. Beyond a typically small angle of incidence, transients generated by a disturbance crossing the continental slope and coast will be trapped on the shelf by internal reflection. The refraction law for a fast-moving forced wave crossing an ocean ridge at greater than a small angle of incidence also results in trapped free-wave transients with tsunami-like periods propagating along the ridge. The subcritical resonance, excitation of shelf modes and trapping of the transients may have implications for storm surges and the generation of destructive meteotsunami.