Influence of Bottom Friction on Sea Surface Roughness and Its Impact on Shallow Water Wind Wave Modeling

Abstract

Using a selected subset of the measured data obtained in shallow waters near Vindeby, Denmark, during RASEX (Risø Air–Sea Experiment), the role of bottom friction dissipation in predicting wind waves (not swell) is assessed with a third-generation numerical wind wave model. The RASEX measurement site is located in relatively shallow waters (depths of about 3 to 4 m) in an area where the waves are predominantly fetch limited (i.e., maximum fetch of about 20 km). The bottom friction dissipation source term is modeled using the linearized bottom friction formulation. This formulation contains a dissipation coefficient, Cf, which depends on wave and sediment properties. In the numerical investigations, we considered three cases: (i) a constant value for Cf as obtained in the JONSWAP Experiment, (ii) a constant geometric roughness kN, and (iii) a constant median sediment size, d50. In the latter case, the bed is treated as a mobile bed and the geometric roughness is related to the dimensions of wave-formed ripples, which is calculated using the empirical expressions of Nielsen. These three cases are investigated using (i) the measured surface winds, U10 (where Janssen's theory is used to calculate sea roughness and the corresponding wind stress), and (ii) the measured wind friction speeds, u∗. Numerical investigations for idealized test cases show that bottom friction dissipation keeps the waves young. This results in high values of sea roughness, wind stress, and wind input source term when Janssen's theory for the coupling between waves and wind stress is used. Using the RASEX dataset, it is shown that Janssen's theory gives too high sea roughness in shallow water. A constant Charnock parameter of 0.015 was found to be better for the event with strong winds. In order to obtain a good agreement between measured and calculated significant wave heights, it was found necessary to use a variable bottom dissipation formulation, where the bottom dissipation coefficient depends in a realistic manner on the hydrodynamic and sediment parameters. The mobile bed friction model with d50 = 0.25 mm gave almost the same results as the constant geometric roughness model with kN = 0.04 m and are both definite improvement over the constant Cf model (JONSWAP friction model), as has been found elsewhere. This approach gave a dissipation coefficient nearly three times the JONSWAP value.