Effects of Long Waves on Wind-Generated Waves

Abstract

A model is developed to explain the observation made in several laboratory experiments that short wind-generated waves are suppressed by a train of long, mechanically generated waves. A sheltering mechanism is responsible for generation of the short wind waves, by which wave growth is proportional to the local turbulent wind stress. Hence, if the turbulent wind stress near the surface is reduced by the long wave, then the short wind wave amplitude, and hence also the energy in the short waves at a given fetch, is lower than in the absence of long wave. A quantitative model of this process is formulated to examine the ratios of the growth rate and the total energy density of wind waves with and without a long wave, which is shown to agree reasonably well with the laboratory experiments. The model also explains why this suppression of wind waves by a very long swell is not observed in the ocean where the effects of swell on wind waves are extremely difficult to detect. In the model, the reduction in the turbulent wind stress by the long wave is largest for small values of CL/u* (where CL is the phase speed of the long wave and u* is the friction velocity of the wind). When this ratio is larger than about 25 (typical of ocean swell), both the reduction of the turbulent wind stress by the long wave and, consequently, the reduction in the total energy density of the wind waves are very small, which explains why this phenomenon has not yet been observed on the ocean.