Fluctuating circulation forced by unsteady multidirectional breaking waves

Abstract

In this paper, we consider nearshore rotational currents directly forced by unsteady multidirectional wave breaking. Scaling relationships, simplified analytical solutions, and asymptotic limits are developed for the maximum forced cross-shore and longshore velocities. In all cases, forced longshore velocities are considerably larger than cross-shore velocities. On longshore-uniform beaches, strong fluctuating velocities are found for (i) large waves; (ii) strong directional spreading; and (iii) short peak wave periods. When topographic inhomogeneities control longshore scales of wave breaking, overall scaling changes and the largest fluctuating velocities are found for ($a$) large waves; ($b$) long wave periods; and ($c$) topographic features that vary quickly in the longshore direction. The ratio of fluctuating rotational velocities to mean longshore current does not depend on the wave height or period, but instead on the bottom friction, slope, deep water wave angle, and details of the wave spectrum.