Directional slope and curvature distributions of wind waves

Abstract

The slope and curvature distributions of wind waves along two principal axes (upwind-downwind and cross-wind) have been measured in a laboratory tank under various wind velocities. In both directions, the slope distributions are very closely Gaussian, and the components of the mean-square water-surface slope vary loga,rithmically with the friction velocity of the wind. As the windvelocityincreases, the ratio of the upwind-downwind and cross-wind components increases and lies between 0.5 and 0.6 at high wind velocities in the gravity-governed regime of wind-wave interaction. The radius of .water-surface curvature, along either direction of measurement, is generally found to be greater at a steeper viewing angle from the normal to the mean water surface. The average radius of curvature of the disturbed surface varies inversely with the friction velocity of the wind. The ratio of the upwind-downwind and cross-wind components of the average radius of curvature is unity at all wind velocities, indicating that the wind-disturbed water surface is isotropic on the smallest scale. Other results show that both the slope and the curvature distributions are asymmetric along the upwind-downwind direction, either because of the presence of parasitic capillaries or because of the occurrence of wave breaking. The results also indicate that even the high frequency portion of the spectrum is saturated locally but the spectrum is not universal, and that the long waves suppress the growth of the nearly saturated ripples.