On the cascade mechanism of short surface wave modulation

Abstract. Modulation of short surface ripples by long surface or internal waves by a cascade mechanism is considered. At the first stage, the orbital velocity of the long wave (LW) adiabatically modulates an intermediate length nonlinear gravity wave (GW), which generates a bound (parasitic) capillary wave (CW) near its crest in a wide spatial frequency band. Due to strong dependence of the CW amplitude on that of the GW, the resulting ripple modulation by LW can be strong. Adiabatic modulation at the first stage is calculated for an arbitrarily strong LW current. The CWs are calculated based on the Lonquet-Higgins theory, in the framework of a steady periodic solution, which proves to be sufficient for the cases considered. Theoretical results are compared with data from laboratory experiments. A discussion of related sea clutter data is given in the conclusion.