Resonant interactions among capillary-gravity waves

Abstract

The analysis presented here is a second-order analysis of the resonant interactions triads of waves with wavelengths in the capillary-gravity and pure capillary ranges. The analysis is not a power series perturbation analysis, and one of the objects is the removal of the secularity which arises through power series perturbations. It is further found that the interactions are energy-conserving to the order considered here. Suitable modifications are made to accommodate the inevitable viscous attenuation associated with these small wavelengths. A start is made toward describing more completely the various spectra of random seas in wave-number and frequency regions where these interactions are dynamically significant.