Measurements of the interaction of wave groups with shorter wind-generated waves

Abstract

Fields of statistically steady wind-generated waves produced in the NASA-Wallops wind wave facility, were perturbed by the injection of groups of longer waves with various slopes, mechanically generated at the upwind end of the tank. The time histories of the surface displacements were measured at four fetches in ensembles consisting of 100 realizations of each set of experimental conditions, the data being stored and analysed digitally. The overall interaction was found to have four distinct phases. (i) When the longer waves overtake the pre-existing wind-generated waves, during the first half of the group where successive crests are increasing in amplitude, vigorous wave breaking near the crests reduces the energy density and $\overline{\zeta^2}$ in the wind waves while straining by the orbital velocities of the group reduces their wavelengths near the crests; the ‘significant slope’ $2\pi(\overline{\zeta^2})^{\frac{1}{2}}/\lambda $ at the crests is found to be very nearly constant and equal to the initial, undisturbed value. After the maximum wave of the group has passed, breaking appears to virtually cease but the earlier energy loss results in suppression of the short waves. The overall suppression by a group of waves is significantly less than that measured by Mitsuyasu (1966) and Phillips & Banner (1974) in a continuous train of waves whose slope is equal to the maximum in the group. A simple description of this phase of the interaction, involving constant significant slope of the breaking waves over the leading half of the group and conservation of action thereafter, gives suppression ratios close to those measured. (ii) Once the group has passed, the surface is much smoother and the waves begin to regenerate under the continued influence of the wind but at rates considerably slower than those suggested by Plant's formula, using the averaged value of u_*. This is qualitatively consistent with a locally reduced surface stress as the wind blows from rougher water well behind the group to the smoother surface immediately behind it. (iii) The regeneration is interrupted by the arrival of a wave energy front moving down the tank, across which the energy density rises abruptly to values up to six times greater than in the undisturbed field. At the same time, the dominant frequencies just behind the wave energy front are lower than in the initial field, and the significant slope $(\overline{\zeta^2})^{\frac{1}{2}} \sigma^2/g $ is, within experimental uncertainty, again identical to that in the initial field. The front was found to propagate notably faster than the appropriate group velocity (g/2σ) and it is suggested that this is the combined result of dispersion, nonlinearity and wind amplification, together with wind-induced drift in the tank. Finally, (iv) the energy density gradually subsides and the dominant wave frequency increases as the wind waves relax towards their undisturbed state, the relaxation seeming to be essentially complete when energy packets arriving at a point have originated at the upwind end of the tank, rather than at the wave energy front.