Measurements of the modulation of short waves from image sequences

Three image processing techniques are described to measure the modulation of the amplitude, phase speed, frequency, and wavenumber of short waves as a function of the phase of the long wave. First, long and short waves are separated by appropriate bandpass filtering. Secondly, the phase speed is computed by determining the local orientation in the space-time domain. Thirdly, Hilbert filters are used to compute the phase and amplitude of the long and short waves. Local wavenumbers and frequencies can then be estimated from spatial and temporal phase gradients, respectively. These techniques are successfully used to analyze long wave/short wave interaction of mechanically generated waves in the glass-wall wave channel at the Scripps Hydraulic Facility and the modulation of short wind waves by larger waves in the large wind-wave flume of Delft Hydraulics (The Netherlands).