RANDOM WAVES ON A VERTICALLY-SHEARED CURRENT

Abstract

This paper considers the interaction between two-dimensional random waves and a co-linear, depth-varying, current. Two rotational wave-current models, capable of incorporating the effects of a depth dependent vorticity distribution, are combined with a conservation equation describing the total energy flux. This provides new solutions capable ofpredicting the change in a wave spectrum due to the interaction with a current. Comparisons between these solutions and a new data set confirms that a successful wavecurrent model must incorporate both the Doppler shift associated with the surface current and the near-surface vorticity distribution. Typical design calculations, based on a uniform current approximation, commonly satisfy neither of these constraints. Accordingly, they are shown to provide a poor description of the laboratory data. Furthermore, the nature of the wave-current interaction, which is shown to be significantly larger than the nonlinear wave-wave interactions, involves both a currentinduced change in the wave motion and a wave-induced change in the current. While the former is reasonably well understood, the latter remains difficult to predict. Indeed, both parts of this overall interaction are shown to be strongly vorticity dependent.