Abstract
The flow composed of a periodic wave motion with turbulent fluctuations caused by breaking and a (slowly varying) mean current is considered. The mean current consists of the combined cross-shore and longshore current velocities generated by the waves which means the profile of the total velocity is highly three dimensional. The Reynolds equations for the currents are derived and the influence of cross-shore and longshore currents on one another is neglected. For the special case of a cylindrical coast and turbulent shear stresses modelled by an eddy viscosity, the equations for the longshore velocity variation V( x, z) over depth and distance from the shore are found to satisfy a Poisson equation. A perturbation solution is derived to a second order for V( x, z) and the classical solutions for V( x) from the literature are found to be logically related to the new solution, which (briefly described) always yields somewhat larger velocities. Measurements in the literature show the same qualitative variation of the longshore velocity over depth but a detailed comparison is not made.
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