Effects of Wave Angle and Lateral Mixing on the Longshore Current

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Abstract
An analytic model of the steady longshore current on a plane beach is presented which includes the effects of wave refraction, lateral mixing and an angle-dependent bottom friction force linear in the current velocity. The formulation is based on the model of Longuet-Higgins2), and isolates the contributions due to a moderately large incident wave angle, and to the mixing parameter, P. A modified definition of the linear bottom friction approximation is proposed, namely that the maximum measured or predicted longshore current be reasonably small in comparison to the amplitude of the wave orbital velocity; former treatments use an over-conservative ratio of the theoretical velocity maximum at the breaker line in the absence of mixing to the amplitude of the wave orbital velocity. The angle dependencies of several important quantities such as the location of the maximum, midsurf and breaker line current velocities are calculated and used to discuss some reasons for the apparent validity of the CERC3) longshore sediment transport formula over a wide range of surf conditions. Values of both the bottom friction and lateral mixing coefficients are determined by fitting the theory to the data.

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