On the Relative Importance of Wind Forcing and Nonlinear Interactions in the Downshift of a Gravity Wave Wavenumber Spectrum

Under wind forcing, the deep water gravity wave amplitude spectrum experiences a shift of the spectral peak and its neighboring wave numbers toward lower wave numbers (downshift). This downshifting as the waves respond to a wind field is widely believed to be caused by the nonlinear interactions that govern the intrinsic wave dynamics. We investigate this process by integrating the Krasitskii equations in the presence of driving and dissipation. These equations make no a priori assumptions regarding the wave amplitude probability distribution function. Numerical results indicate that while nonlinear interactions play a role, the dominant cause of the downshift is the functional dependencies on wave number which are at the very least required for such a wind forcing term to have the correct dimensions.