Wave‐current interaction in nearshore shear instability analyzed with a vortex force formalism

Abstract

We examine wave‐current interactions in littoral current shear instabilities above a single‐barred beach using a fully coupled wave and barotropic current model based on the multiscale asymptotic theory derived by McWilliams et al. (2004). This Eulerian wave‐averaged model captures wave effects on currents (WEC) in a manner that leads to simple interpretations. The dynamically conservative WEC are the vortex force and material transport by Stokes drift and the sea level adjustment by wave set‐down and setup. In the setting considered here there are also important current effects on the waves (CEW): induction of a Doppler shift by currents and surface elevation variation in the wave dispersion relation. Nonconservative effects, due to wave breaking and bottom drag, also play a prominent role in generating and equilibrating the mean alongshore current, consistent with prior studies. High bottom drag stabilizes the currents, while a drag reduction below a critical threshold value leads to shear instability with nearly periodic, alongshore‐fluctuating eddies. An even smaller bottom drag yields irregular eddy motions with intermittent offshore eruption of vortex pairs from the meandering alongshore current. Several alternative parameterizations of the bottom drag are contrasted here. Including CEW in the model leads to a delay in the onset of the instability, a suppression of fluctuations in cross‐shore velocity and lateral Reynolds stress, and an enhancement of the mean alongshore velocity. The WEC increase the Reynolds stress in the offshore region, and the conservative vortex force and mean advection are comparable in magnitude to the breaking acceleration and bottom drag. Conversely, the CEW reduce the Reynolds stress and attenuate the breaking acceleration through refractive focusing by current shear. Overall, the WEC enhance the instantaneous cross‐shore momentum flux to induce more energetic eddy motions and retard the mean alongshore current, while the CEW stabilize the fluctuations and help maintain a strong mean current.