Numerical investigation of wind input and spectral dissipation in evolution of wind waves.

Abstract

The present study comprised an intensive investigation of the two newly proposed parameterisation forms for the wind input source term S[subscript]in (Donelan et a1., 2006) and the wave dissipation source term S[subscript]ds (Young and Babanin, 2006) proposed on the basis of the recent experimental findings at Lake George, New South Wales, Australia in 1997-2000. The main objective of this study was to obtain advanced spectral forms for the wind input source function S[subscript]in and wave spectral dissipation source function S[subscript]ds, which satisfy important physical constraints. A new approach was developed to achieve the objectives of this study, within the strong physical framework. This approach resulted in a new balance scheme between the energy source terms in the wave model, mentioned before as the split balance scheme (Badulin, 2006). The wave-induced stress was defined as the main physical constraint for a new wave model including recently suggested source functions for the wind input and wave dissipation source terms. Within this approach, a new methodology was developed for correction of the wind input source function S[subscript]in. Another important physical constraint was the consistency between the wave dissipation and the wind energy input to the waves. The new parameter, the dissipation rate, R, was introduced in this study, as the ratio of the wave dissipation energy to the wind input energy. The parameterisation form of the dissipation rate is presented as a function of the inverse wave age U ₁₀ / c[subscript]p Some aspects of wave spectral modelling regarding the shape of the wave spectrum and spectral saturation were revised. The two-phase behaviour of the spectral dissipation function was investigated in terms of the functional dependency of the coefficients a for the inherent wave breaking term and b for the forced dissipation term. The present study found that the both coefficients have functional dependence on the inverse wave age U ₁₀ / c[subscript]p and the spectral frequency. Based on the experimental data by Young and Babanin (2006), a new directional spreading function of bimodal shape was developed for the wave dissipation source term. The performance of the new spectral functions of the wind input S[subscript]in(f) and the wave dissipation S[subscript]ds(f) source terms was assessed using a new third-generation two-dimensional research wave model WAVETIME-I. The model incorporating the corrected source functions was able to reproduce the existing experimental data.