Application of Fourier Transform-based Cross-correlation in Determining Breaking Water Wave Phase Velocity from Station-to-Station Free Surface Elevation Time Series

Water waves were generated in a laboratory wave flume that propagated and broke as plunging
waves on a 1:20 beach slope. Free surface elevation time series were then measured along the flume
in order to determine changes in wave characteristics as the waves propagated from deep water to the
shore. A pair of parallel-wire capacitive wave gages was used to simultaneously measure free surface
elevations at different positions along the flume. One gage was kept fixed near the wave generator
to provide a reference while the other was moved in steps of 0.1 m in the vicinity of the break
point. Data from these two wave gages measured at the same time constitute station-to-station free
surface elevation time series. Fast Fourier Transform (FFT) based cross-correlation techniques were
employed to determine the time lag between each pair of the time series. The time lag was used
to compute the phase shift between the reference wave gage and that at various points along the
flume. Phase differences between two points spaced 0.1 m apart were then used to calculate local
mean wave phase velocity for a point that lies in the middle. Results show that moving from deep
water to shallow water, the measured mean phase velocity decreases almost linearly from about
1.75 m/s to about 1.50 m/s at the break point. Just after the break point, wave phase velocity
abruptly increases to a maximum value of 1.87 m/s observed at a position 30 cm downstream of
the break point. Thereafter, the phase velocity decreases, reaching a minimum of about 1.30 m/s.