Interaction of capillary waves with longer waves. Part 2. Applications to waves in two surface dimensions and to waves in shallow water

Abstract

In Part 1 of this work we presented a new mathematical formulation for numerical investigation of capillary wave dynamics. This permitted calculations to be readily performed on a desktop computer. Applications given were primarily to waves in one surface dimension. In Part 2 we describe further applications to waves in two surface dimensions and also to waves in shallow water (not, however, shallow for the capillary waves). Wavenumber–frequency spectra for wind waves are calculated. As was observed in tank experiments by Hara et al. (1997), our calculations show both a frequency spread and a frequency up-shifting which suggests that capillary waves are ‘dragged along’ by longer waves. Fine-scale roughness near wind wave crests shows a transitory nature, changing with the wave pattern. We discuss implications of this for microwave remote sensing. The propagation of short gravity waves in shallow water is studied. As these waves develop bore-like forward faces, generation of parasitic capillary waves is observed. Generation rates for these are substantially greater than observed for waves in deep water.