On mass transport in deep water waves

Summary Various formulations of the mass-transport problem are compared for progressive waves in deep water. In order to calculate the mass-transport velocity as a function of depth in the main body of the fluid, it is necessary to include the effect of viscous wave attenuation. It is shown that the usual assumptions of periodicity in distance and attenuation with time or periodicity in time and attenuation with distance, are both physically unsatisfactory. The first does not specify a unique solution, and the second is incompatible with the assumption of zero surface stress. A certain critical constant tangential wind stress will maintain strictly time-periodic deep water waves. The corresponding attenuation with distance is then calculated to order ³. A constant tangential stress greater or less than the critical causes waves, necessarily decaying with distance, to grow or decay with time.