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 ϕ¯² ∝ ∫ ϕ_δ²dt, where ϕ_δ is the response to impulsive forcing and the integral is over the record length. The rms response therefore initially increases with time as t^½, and reaches stationarity in the decay scale for ϕ_δ. As in the random-walk problem, the t^½ 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 ϕ_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.