Approximations for Surface Waves in Strongly-sheared Coastal Current Systems

Abstract:

Currents driven by tides or wind forcing in coastal areas may often be strongly sheared in the vertical direction due to the interactions of fresher coastal discharges with ambient shelf waters. There is generally no closed form analytic solution describing wave motion for the case of an arbitrary vertical distribution of horizontal mean (or wave-averaged) current. Consequently, a variety of perturbation methods have been developed over the years to provide approximations for the kinematic properties of surface waves, usually in terms of a depth-weighted, frequency-dependent average of the current velocity.

Recently, we have described approximations for group velocity, action density and action flux for monochromatic waves propagating over a current field with arbitrary depth variation, and have suggested strategies for representing the frequency-dependent results compactly in the specification of current effects on waves in coupled current and wave modules in ocean modeling systems (Banihashemi et al., 2017; Banihashemi and Kirby, 2019). In this presentation, we concentrate on wave effects on currents, and develop a model for wave forcing on currents in 3D, developing approximations that are consistent with the description of the wave field resulting from the perturbation approach. We compare our results with the model of McWilliams et al. (2004) for the case of weak current shear, and then evaluate the model's usefulness for the case of stronger shear by comparing to the full results for a current with constant shear. Finally, numerical examples for more realistic current distributions are illustrated.

Banihashemi, S., Dong, Z. and Kirby, J. T., Ocean Modelling, 116, 33-47, 2017.

Banihashemi, S. and Kirby, J. T., Ocean Modelling, 143, 101460, 2019.

McWilliams, J. C., Restrepo, J. M. and Lane, E. M., J. Fluid Mech., 511, 135-178, 2004.