Eulerian and Lagrangian aspects of the longshore drift in the surf and swash zones

Abstract

A theoretical study of the mean longshore mass flux and longshore drift velocities due to waves obliquely incident on a uniform sloping beach is presented. Analysis is performed using both Eulerian and Lagrangian representations of the flow. A number of results based on inviscid solutions are obtained concerning the mean longshore mass flux 〈My〉 inside the swash zone. Thus 〈My〉 depends on the parameters (wave amplitude, wave frequency, and wave number) of waves incident at a shoreline in a similar fashion to the dependence of the mass flux occurring between the crests and troughs of propagating waves on the same wave parameters. The mass flux depends on the square of the local wave amplitude, even for very steep waves which break before reaching the shoreline. A Lagrangian approach shows that particle paths are not closed even offshore of the breaking point and that “zigzag transport” is characteristic of Lagrangian particle paths in the two‐dimensional horizontal flow seaward of the swash zone. The cross‐shore profile of the longshore drift velocity is analyzed. Very weak longshore drift velocity characterizes the nonbreaking waves up to the swash zone. Onshore of the breaking point we find that the longshore drift velocity has a quasi‐linear profile up to the maximum velocity reached near the shoreline. Effects of seabed friction are included in the computation of cross‐shore profiles of the longshore drift velocity. A sensitivity analysis reveals that even for relatively small friction parameters (ƒ≈0.1), velocities inside the swash zone are greatly reduced. The reduction in longshore drift velocity is greater for the Lagrangian profile than for the Eulerian one, and for larger friction parameters (ƒ≥0.1) the maximum longshore velocity moves toward the breaking point, where the friction effects are smaller. Finally, steady state profiles of the longshore drift velocities (Eulerian and Lagrangian) are computed.