Depth Dependence of Nearshore Currents and Eddies

Abstract

The three-dimensional (across-shore, alongshore, and vertical) structure of hourly mean currents and <0.01 Hz eddies was measured on a natural beach using 12 Acoustic Doppler Profilers. Both eddies and alongshore currents became relatively depth-uniform inside the surfzone. Eddies showed greater depth dependence than alongshore currents. A two-layer model, derived by scaling of the wave-averaged shallow water equations, yielded separate equations for depth-averaged and depth-dependent velocity components. Scaling suggests, and observations confirm, only a small role for lateral advection in most surfzone cases, leading to one-dimensional vertical models for depth dependence. For alongshore currents, depth dependence is generated by opposite forcing on lower and upper layers, respectively by bottom friction (quantified by time scale λ-1b) and waves or wind. This generation is balanced by mixing between upper and lower layers (time scale λ-1m), so the ratio between depth-dependent and depth-averaged alongshore currents equals λb/λm. Established models for bottom friction and breaker-induced mixing predicted a surfzone reduction in λb/λm consistent with the observed reduction in alongshore current depth dependence. Scatter around trends was considerable. Alongshore variability was significant for depth-dependence of currents and eddies. Inside (but not outside) the surfzone, the mixing time scale λ-1m was shorter than the eddy period, so a quasi-steady balance was predicted between forcing and mixing of eddy depth dependence. Observed eddy depth dependence exceeded predictions for barotropic eddies generated by shear production (i.e., shear instabilities), possibly indicating generation of eddies by random breaking waves in the surfzone, or indicating baroclinic effects outside the surfzone.