Waves and strongly-sheared currents: extensions to coastal ocean models
Date
2019
Authors
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Publisher
University of Delaware
Abstract
Interaction between surface gravity waves and mean flows has implications for wave propagation, breaking and changes in the mean circulation pattern. These physical processes subsequently modify material transport and mixing in the coastal ocean. Most of the existing wave-current interaction modeling approaches are based on the assumptions of weak current or strong current with weak vertical shear. Few of the former studies consider the interaction of waves with strongly sheared current, in which the current vertical shear can affect linear wave dynamics at the leading order. In real world, however, in coastal zones where fresh riverine water meets salty seawater, such as in a river mouth, flow structures can be highly complex and the current becomes strongly sheared due to stratification and tidal effects. ☐ In this study we investigate the shortcomings in numerical modeling of waves and vertically sheared currents. The influence of an arbitrary current profile on wave dispersion and evolution equation is studied. We demonstrate that the widely used depth-weighted average current value of Kirby & Chen (1989, KC89), is not the correct current speed to use directly in the action equation in SWAN or similar wave models, as this approach neglects the contribution from the derivative of the wavenumber-dependent weighted current during calculation of the group velocity. We correct this error and also suggest a strategy for determining the current contribution to group velocity as a function of frequency, employing a Taylor series expansion about the peak frequency, significantly extending the range of accuracy of current information with minimal additional programming or data passage. The expressions for energy density and intrinsic frequency used to construct the wave action density are similarly investigated, using perturbation approximations in the general action balance equation of Voronovich (1976). The results suggest that the action density N=E0/σ may be consistently constructed using the usual expression for energy density, E0=1/2ρga2, together with a σ=ω-kŨ based on the KC89 current speed. The wave action flux approximation also suggests the use of the current Û as the correct current speed to be used in the advection velocity, which is the vector form of the advection velocity suggested by KC89 and discussed by Banihashemi et al. (2017). We have further extended the suggested Taylor expansion around the peak wave number in a modeled spectrum, with extensions covering the specification of action, flux and intrinsic frequency as well as an extension to a general 2D horizontal setting. These results provide an avenue for calculating wave action and action flux in spectral wave models, using a compact set of information about the current field evaluated at the spectral peak wave number. Lastly the coupled wave-current model NH(WAVE) ̅, which couples the wave model SWAN with a wave-averaged version of the non-hydrostatic model NHWAVE (Ma-etal-2012), is validated using laboratory experiments on wave-current interaction. We have chosen the experiments done by Kemp & Simons (1982) on the interaction of non-breaking waves with currents in a laboratory flume. The results from our 3D non-hydrostatic model agree reasonably well with data from the experiment for wave following currents.