Gravity-Capillary Wave Spectral Modulation by Gravity Waves

Abstract

In order to more fully understand the specific hydrodynamic relationship between young wind-generated gravity-capillary waves and longer gravity waves, a laboratory experiment was devised to observe changes in short wave spectral behavior over the phase of a long wave. This paper endeavors to expand on the body of laboratory wave modulation data and extend the investigation in support of the radar remote sensing of ocean surface waves. Measurements were made in the University of Miami’s surge–structure–atmosphere interaction facility in the air–sea interaction saltwater tank wind-wave tank, with 10 m referenced wind speeds ranging between 5 and 23 m/s and paddle-generated wave steepnesses “ak” varying between $0.05 . A polarimetric camera was used to capture high sampling frequency maps of wave slope, yielding spatiotemporal information about short wind-wave behavior [provided as temporal variations in the wavenumber spectrum, where $k~\approx \mathscr {O}$ (100–1000) rad/m]. The simultaneous and colocated long wave phase was measured via a side-looking camera. Hydrodynamic modulation transfer function (MTF) phases are found to be in general agreement with established values (between 2 and 10 radians) at the given wind speeds. The positive phase of the modulation places it immediately downwind of the long wave crest, with MTF magnitudes strongest for high wavenumbers at the lowest wind speeds. The results are also presented to show the modulation of gravity-capillary and pure capillary waves as variations in mean square slope over the long wave phase, with peak roughness enhancement found to move upwind of the long wave crest with increasing wind forcing.