Nonlinear wave interactions in supersonic wind-generated waves

Abstract

A nonlinear analysis is presented for the case of second-harmonic resonant interactions on the interface of a liquid film and a supersonic gas stream. The analysis takes into account the effects of the gas viscosity and mean profiles. Moreover, the extent of the gas disturbance layer is not restricted to the region in which the mean profiles are linear. Self-sustained oscillations are calculated for low and intermediate liquid Reynolds numbers. The present solution is compared with available experimental data. The predicted and observed wave amplitudes, wavenumbers, and frequencies are in good agreement for intermediate liquid Reynolds numbers. The calculated amplitudes overpredict the observed values by about a factor of three for low liquid Reynolds numbers.