Generation of initial wavelets by instability of a coupled shear flow and their evolution to wind waves

Abstract

The generation of initial wavelets, which appear at the initial stage of the generation and growth processes of wind waves after the abrupt start of the wind on a still water surface, has been investigated by systematic experiments together with theoretical analyses. The energy of the initial wavelets, measured by a resistance-type wave gauge of 50 μm diameter, grew exponentially with time at a constant frequency. The frequency and the growth rate were independent of the fetch but did depend on the friction velocity u*a of the air. The phase velocity of the initial wavelets, measured by a shadowgraph-photography technique, was nearly constant, independent of u*a. A coupled shear flow model in the air and water was examined, to explain the observed characteristics of the initial wavelets in terms of the instability mechanism. The theoretical analysis showed that, for each shear flow pattern observed in the experiments, there exist waves whose growth rate is maximum. The frequency, the growth rate and the phase velocity of these critical waves were virtually coincident with those properties of the observed initial wavelets. It is concluded that the generation of wind waves, whose initial stage is called the initial wavelets, is caused by the selective amplification, by the instability mechanism, of the small perturbations which inevitably occur in the flow.The limitation of the linear instability theory as applied to the process of further growth of the wind waves is also discussed. From some facts recognized through detailed observations, it is inferred that the phenomena controlled by the linear mechanism last for only about 10 s, and that these evolve to the wind waves which are characterized by inherent nonlinearity.