SHEAR INSTABILITY OF LONGSHORE CURRENTS - A NUMERICAL STUDY

Temporal variations of longshore currents have recently been identified on natural beaches (Oltman-Shay et al., 1989). Termed shear waves, these variations appear to be strongly linked to the strength of the mean longshore current. Bowen and Holman (1989) proposed a simple model based on the shear instability of a steady bilinear longshore current profile over a constant depth to explain these observations. In this work we generalize Bowen and Holman's model. A numerical solution technique is employed to study the characteristics of shear waves generated by instabilities of smooth longshore current profiles on general bottom topographies. We find that the stability characteristics are extremely sensitive to variations in the bottom topography. The "dispersion" relationship of the shear waves is almost linear and does not seem to be very sensitive to the topography. We find that the presence of a nearshore bar greatly enhances the strength of the instability and, in certain situations, tends to trap the shear wave shoreward of the bar crest. The results also suggest that the shear on the seaward face of the longshore current profile is an important parameter in the stability problem. A Fjortoft condition is established for the instability equation. Estimates of length and time scales indicate that shear waves should be detectable in laboratory experiments. An order of magnitude analysis indicates that shear waves may be a plausible mixing mechanism in the nearshore region.