The Role of Evolution Mechanisms in the Formation of a Wind-Wave Equilibrium Spectrum

The formation of a stationary (equilibrium) range in a wind-wave spectrum is investigated by numerical simulation. The equation of evolution of the wind-wave spectrum is solved using the exact calculation of the Hasselmann kinetic integral and involving various modifications of known parameterizations of the mechanisms of wave pumping by wind (In) and of wave dissipation (Dis). It is shown that it is these two mechanisms that are responsible for the shape of the stationary range of the wind-wave spectrum, whereas the nonlinear mechanism plays a stabilizing but subsidiary role. With an appropriate choice of mathematical representations for In and Dis, any known empirical shape of the stationary range of the spectrum can be obtained. During the calculations it is found that, for real wind waves, the known representations of In and Dis do not ensure the existence of the inertial interval required for Kolmogorov-type spectra formation due to the nonlinear interactions between waves.