Shear instabilities of the mean longshore current : 1. theory

copyrighted by American Geophysical UnionA new class of nearshore waves based on the shear instability of a steady longshore current is discussed. The\ud dynamics depend on the conservation of potential vorticity but with the background vorticity field, traditionally\ud the role of Coriolis in larger scale flows, supplIed by the shear structure of the longshore current. The resulting\ud vorticity waves are longshore-progressive with celerities roughly equal to V₀/3, where V₀ is the peak longshore\ud current velocity. A natural frequency scaling for the problem is fs, the shear of the seaward face of the\ud longshore current. While the instability can span a range of frequencies and wavenumbers, a representative\ud frequency is given by 0.07 fs, typically in the range of 10¯³-10¯² Hz (called the Far Infragravity, or FIG, band\ud because frequencies are just below those of the infragravity band). Wavelengths are of the order of 2x₀, where X₀\ud is the width of the longshore current. Growth is exponential with an e-folding time that is typically half of a\ud wave period. Field data, presented in the companion paper [Oltman-Shay et al., this issue], demonstrate the\ud presence of energetic motions from a natural beach whose behavior matches the theory in many aspects.\ud Results from the model suggest that shear instability will be more important on barred, rather than monotonic\ud beach profiles, a result of the stronger shears expected over the bar crest. Since vorticity waves will probably\ud have a profound effect on cross-shore mixing as well as longshore current dissipation, we expect the dynamics\ud of barred and monotonic beaches to show fundamental differences