Observations of the directional distribution of the wind energy input function over swell waves

Abstract

Field measurements of wind stress over shallow water swell traveling in different directions relative to the wind are presented. The directional distribution of the measured stresses is used to confirm the previously proposed but unverified directional distribution of the wind energy input function. The observed wind energy input function is found to follow a much narrower distribution (β 3.6θ) than the Plant (1982) cosine distribution. The observation of negative stress angles at large wind-wave angles, however, indicates that the onset of negative wind shearing occurs at about θ 50°, and supports the use of the Snyder et al. (1981) directional distribution. Taking into account the reverse momentum transfer from swell to the wind, Snyder's proposed parameterization is found to perform exceptionally well in explaining the observed narrow directional distribution of the wind energy input function, and predicting the wind drag coefficients. The empirical coefficient (ε) in Snyder's parameterization is hypothesised to be a function of the wave shape parameter, with ε value increasing as the wave shape changes between sinusoidal, sawtooth, and sharp-crested shoaling waves.