Abstract
This paper describes a technique to measure the spatial structure of short capillary–gravity waves on the water surface. The method is based on optical refraction of a single laser beam crossing the air–water interface to derive the surface slope information. By quickly scanning the laser beam, the spatial and temporal evolution of the surface undulation can be studied in great detail. The spatial measurement of the surface fluctuation also allows direct computation of the wavenumber spectra in the capillary–gravity wave regime. This approach avoids the difficulty of resolving the Doppler frequency shift encountered in the processing of high-frequency spectra derived from a single-point sensor. The modulation of short waves by the orbital velocity of surface long waves is analyzed from the distribution of the wavenumber spectra of short waves along the phase of long waves. Key parameters determining the modulation magnitude are identified to be the slope of wavenumber spectra in the neighborhood of the modulated wave component, the ratio of the group and phase velocities of the modulated wave component, the dimensionless relaxation parameter, and the resonance parameter. Quantitative results on these parameters are obtained from the experimental data.
Corresponding author address: Dr. Paul A. Hwang, Code 7332, Oceanography Division, Naval Research Laboratory, Stennis Space Center, MS 39529-5004.
Email: phwang@nrlssc.navy.mil
