Wave-follower field measurements of the wind-input spectral function. Part II: Parameterization of the wind input

Nearly all of the momentum transferred from wind to waves comes about through wave-induced pressure acting on the slopes of waves: known as form drag. Direct field measurements of the wave-induced pressure in airflow over water waves are difficult and consequently rare. Those that have been reported are for deep water conditions and conditions in which the level of forcing, measured by the ratio of wind speed to the speed of the dominant (spectral peak) waves, is quite weak. The data reported here were obtained over a large shallow lake during the Australian Shallow Water Experiment (AUSWEX). The propagation speeds of the dominant waves were limited by depth and the waves were correspondingly steep. This wider range of forcing and concomitant wave steepness revealed some new aspects of the rate of wave amplification by wind, the so-called wind input source function, in the energy balance equation for wind-driven water waves. It was found that the exponential growth rate parameter (fractional energy increase per radian) depended on the slope of the waves, ak, vanishing as ak moved towards 0. For very strong forcing a condition of “full separation” occurs, where the airflow detaches from the crests and reattaches on the windward face leaving a separation zone over the leeward face and the troughs. In a sense, the outer flow does not “see” the troughs and the resulting wave-induced pressure perturbation is much reduced, leading to a reduction in the wind input source function relative to that obtained by extrapolation from more benign conditions. The source function parameterized on wave steepness and degree of separation is shown to be in agreement with previous field and laboratory data obtained in conditions of much weaker forcing and wave steepness. The strongly forced steady-state conditions of AUSWEX have enabled the authors to define a generalized wind input source function that is suitable for a wide range of conditions.