Nearshore mixing and dispersion

Longshore currents have in the past been analysed assuming that the lateral mixing could be attributed to turbulent processes. It is found, however, that the mixing that can be justified by assuming an eddy viscosity $\nu _{t}$ = l$\surd $k where l is the turbulent length scale, k the turbulent kinetic energy, combined with reasonable estimates for l and k is at least an order of magnitude smaller than required to explain the measured cross-shore variations of longshore currents. In this paper, it is shown that the nonlinear interaction terms between crossand longshore currents represent a dispersive mechanism that has an effect similar to the required mixing. The mechanism is a generalization of the one-dimensional dispersion effect in a pipe discovered by Taylor (1954) and the three-dimensional dispersion in ocean currents on the continental shelf found by Fischer (1978). Numerical results are given for the dispersion effect, for the ensuing cross-shore variation of the longshore current and for the vertical profiles of the longshore currents inside as well as outside the surf zone. It is found that the dispersion effect is at least an order of magnitude larger than the turbulent mixing and that the characteristics of the results are in agreement with the sparse experimental data material available.