Laboratory observations of gravity‐capillary waves under transient wind forcing

Abstract

Laboratory experiments were conducted to investigate the response of short wind waves (wave numbers between 50 and 800 rad m−1) under transient wind forcing. Three‐dimensional wave number frequency spectra of gravity‐capillary waves were measured using a scanning laser slope gauge (SLSG). When wind is started rapidly, gravity‐capillary waves of a particular wave number (initial wavelets) first appear, and they are immediately followed by waves over a wider wave number range (both in magnitude and in direction). These waves all appear to grow exponentially, with each wave number growing at its own growth rate. The observed energy input rates from wind to waves are always maximum for along‐wind waves and are smaller for waves in directions oblique to the wind. When wind speed is modulated periodically in time, the modulation of the wind stress lags behind that of the wind speed, and the short wind wave spectra lag further behind the wind stress. Assuming that waves are modulated according to existing relaxation theory and that the relaxation rate is identical to the wave growth rate, very short wind waves appear to respond to the instantaneous wind speed while longer wind waves appear to respond to the instantaneous wind stress.