[OPTICAL REVIEW Vol. 4, No. 5 (1997) 610-619]

Realization of a Gravity-Capillary Wave Surface Using Sub-Nyquist Spectral Samples

Kyu YOSHIMORI,1 Kohzaburo OHNAKA,2 Kazuyoshi ITOH,2 Hiroshi KAWAMURA3 and Yoshiki ICHIOKA4

1Furuno Electric Co., LTD., Ashihara-cho 9-52, Nishinomiya, 662 Japan, 2Department of Applied Physics, Graduate School of Engineering, Osaka University, Yamadaoka 2-1, Suita, 565 Japan, 3Center for Atmospheric and Oceanic Studies, Faculty of Science, Tohoku University, Sendai, 980 Japan, 4Department of Material and Life Science, Graduate School of Engineering, Osaka University, Yamadaoka 2-1, Suita, 565 Japan

(Received November 28, 1996; Accepted June 10, 1997)

A method for numerical realization of a full gravity-capillary wave surface that is specified by a wave-spectral model and a dispersive relationship of the surface wave is developed on the basis of the angular spectral representation of a random water surface. A significant aspect of the method is that it requires a smaller number of spectral samples than that required by the Whitteker-Shannon sampling theorem for the complete generation of a full gravity-capillary wave surface, without resulting in any appreciable errors in auto-correlation functions for the surface displacement or surface slopes. The method enables the unified treatment of gravity and capillary waves in numerical studies of higher order characteristics of the thermal radiation emitted from, and the light scattered by, the wave surface.

Key words : ocean, rough surface, thermal emission, scattering