REALIZATION OF A GRAVITY-CAPILLARY WAVE SURFACE USING SUB-NYQUIST SPECTRAL SAMPLES

A method for numerical realization of a full gravity-capillary wave su rface that is specified by a wave-spectral model and a dispersive rela tionship of the surface wave is developed on the basis of the angular spectral representation of a random mater surface. A significant aspec t of the method is that it requires a smaller number of spectral sampl es than that required by the Whitteker-Shannon sampling theorem for th e complete generation of a full gravity-capillary wave surface, withou t resulting in any appreciable errors in auto-correlation functions fo r the surface displacement or surface slopes. The method enables the u nified treatment of gravity and capillary waves in numerical studies o f higher order characteristics of the thermal radiation emitted from, and the light scattered by, the wave surface.