Shear instabilities of the mean longshore current: 1. Theory

Abstract

A new class of nearshore waves based on the shear instability of a steady longshore current is discussed. The dynamics depend on the conservation of potential vorticity but with the background vorticity field, traditionally the role of Coriolis in larger scale flows, supplied by the shear structure of the longshore current. The resulting vorticity waves are longshore‐progressive with celerities roughly equal to V 0 /3, where V 0 is the peak longshore current velocity. A natural frequency scaling for the problem is f s , the shear of the seaward face of the longshore current. While the instability can span a range of frequencies and wavenumbers, a representative frequency is given by 0.07 f s , typically in the range of 10 −3 –10 −2 Hz (called the Far Infragravity, or FIG, band because frequencies are just below those of the infragravity band). Wavelengths are of the order of 2 x 0 , where x 0 is the width of the longshore current. Growth is exponential with an e ‐folding time that is typically half of a wave period. Field data, presented in the companion paper [Oltman‐Shay et al., this issue], demonstrate the presence of energetic motions from a natural beach whose behavior matches the theory in many aspects. Results from the model suggest that shear instability will be more important on barred, rather than monotonic beach profiles, a result of the stronger shears expected over the bar crest. Since vorticity waves will probably have a profound effect on cross‐shore mixing as well as longshore current dissipation, we expect the dynamics of barred and monotonic beaches to show fundamental differences.