Adjustment of Wind Waves to Sudden Changes of Wind Speed

Abstract

An experiment was conducted in a small wind-wave facility at the Ocean Engineering Laboratory, California, to address the following question: when the wind speed changes rapidly, how quickly and in what manner do the short wind waves respond? To answer this question we have produced a very rapid change in wind speed between Ulow (4.6 m s−1) and Uhigh (7.1 m s−1). Water surface elevation and air turbulence were monitored up to a fetch of 5.5 m. The cycle of increasing and decreasing wind speed was repeated 20 times to assure statistical accuracy in the measurement by taking an ensemble mean. In this way, we were able to study in detail the processes by which the young laboratory wind waves adjust to wind speed perturbations. We found that the wind-wave response occurs over two time scales determined by local equilibrium adjustment and fetch adjustment, Δt1/T = O(10) and Δt2/T = O(100), respectively, in the current tank. The steady state is characterized by a constant non-dimensional wave height (H/gT2 or equivalently, the wave steepness for linear gravity waves) depending on wind speed. This equilibrium state was found in our non-steady experiments to apply at all fetches, even during the long transition to steady state, but only after a short initial relaxation Δt1/T of O(10) following a sudden change in wind speed. The complete transition to the new steady state takes much longer, Δt2/T of O(100) at the largest fetch, during which time energy propagates over the entire fetch along the rays (dx/dt = cg) and grows under the influence of wind pumping. At the same time, frequency downshifts. Although the current study is limited in scale variations, we believe that the suggestion that the two adjustment time scales are related to local equilibrium adjustment and fetch adjustment is also applicable to the ocean.