Generation of Coastal Inertial Oscillations by Time-Varying Wind

Abstract

The excitation of coastal inertial oscillations by a rapidly varying wind is investigated. It is shown that the mean-square response to a completely random forcing is ??2 ? ? ?δ2dt, where ?δ is the response to impulsive forcing and the integral is over the record length. The rms response therefore initially increases with time as t½, and reaches stationarity in the decay scale for ?δ. As in the random-walk problem, the t½ increase is a result of the superposition of uncorrelated steps. Continuous random forcing preferentially increases subsurface amplitudes, since the energy flux from the coast-surface corner causes a surface decay and a subsurface growth of ?δ. With assumed parameters, a step-input wind forcing of 1 dyn cm?-2 generates inertial oscillations of 4 cm s?1 in the surface layer and 0.7?1.5 cm s?1 below. With a random wind in the range (?0.5, 0.5) dyn cm?2, the surface values increase to 8?11 cm s?1 and the subsurface values to 3?7 cm s?1. With an observed wind-forcing the surface and subsurface amplitudes are 10?17 cm s?1 and 5?9 cm s?1, respectively. Compared to the step-input wind, the oscillations due to a randomly varying wind are less coherent in the vertical and more intermittent in time.