Mixing parameterization: Impacts on rip currents and wave set-up

Wave set-up is often underestimated by the models (e.g. Raubenheimer et al., 2001). Our paper discusses how the wave set-up may be changed by the inclusion of turbulent mixing in the bottom shear stress. The parameterization developed in Mellor (2002) for phase-averaged oscillatory boundary layer is used for this purpose. Two studies are carried out. The dependence of the parameterization on the vertical discretization and on the magnitude of the near-bottom wave orbital velocity is investigated. The function that distributes the turbulent terms over the vertical is modified, giving a good agreement with the average of the phase-resolved velocities, but an overestimation of the turbulent phase-resolved velocities. Applying that parameterization to simulate laboratory conditions in the presence of rip currents gives accurate magnitudes of the rip velocity, particularly in a fully coupled wave-current configuration, with an RMS error of about 4%. Compared to a model using the more standard Soulsby (1995) parameterization, the wave set-up is increased by about 12% when using the alternative parameterization. Thus the bottom shear stress is sensitive to the mixing parameterization with a possible effect of turbulence on the wave set-up. Further measurement and parameterization efforts are necessary for practical applications.