A study of advection of short wind waves by long waves from surface slope images

Abstract

Spatial and temporal measurements of short wind waves can be obtained by laser scanning slope gauges and surface slope imaging detectors in the recent development of optical techniques. Slope image data from wind wave experiments in wind wave facilities at Heidelberg and Marseille are used to study the propagation of short wind waves. The data were acquired by an interlaced CCD camera. Each pair of images is consisted of odd and even video fields that are 1/60 second apart. The propagation speed of short wavelets can thus be measured directly through tracking wavelets between a pair of the field images. The images are filtered into different spatial scales. The pairs of the spatial components are matched up for estimating the propagation speeds of waves at different wavelengths. The shortest waves are parasitic capillaries which are capable of matching the speed of long waves. They are quasi-stationary relative to the crest of the long wave within our measurement accuracy. This suggests that the group velocity of parasitic capillaries must be in near balance with the local orbital velocity of the underlying long wave. The waves of different lengths propagate, on the average, at different speeds proportional to the dispersion relation, and are not locked into the long wave phase speeds. There is a large variation in the propagating speeds due to the orbital advection by long waves.