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

摘要

We examine wave-current interactions in littoral current shear instabilities above asingle-barred beach using a fully coupled wave and barotropic current model based on themultiscale 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 simpleinterpretations. The dynamically conservative WEC are the vortex force and materialtransport by Stokes drift and the sea level adjustment by wave set-down and setup. In thesetting 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 wavedispersion relation. Nonconservative effects, due to wave breaking and bottom drag, alsoplay a prominent role in generating and equilibrating the mean alongshore current,consistent with prior studies. High bottom drag stabilizes the currents, while a dragreduction below a critical threshold value leads to shear instability with nearly periodic,alongshore-fluctuating eddies. An even smaller bottom drag yields irregular eddy motionswith intermittent offshore eruption of vortex pairs from the meandering alongshorecurrent. 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 suppressionof fluctuations in cross-shore velocity and lateral Reynolds stress, and an enhancement ofthe mean alongshore velocity. The WEC increase the Reynolds stress in the offshoreregion, and the conservative vortex force and mean advection are comparable inmagnitude to the breaking acceleration and bottom drag. Conversely, the CEW reduce theReynolds stress and attenuate the breaking acceleration through refractive focusing bycurrent shear. Overall, the WEC enhance the instantaneous cross-shore momentum flux toinduce more energetic eddy motions and retard the mean alongshore current, while theCEW stabilize the fluctuations and help maintain a strong mean current.