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Cross-Correlation of Station-to-Station Free Surface Elevation Time Series for Breaking Water Waves

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Abstract: Free surface elevation time series of breaking water waves were measured in alaboratory flume. This was done in order to analyze changes in wave characteristicsas the waves propagated from deep water to the shore. A pair of parallel-wire capacitive wave gages was used to simultaneously measure free surfaceelevations at different positions along the flume. One gage was kept fixednear the wave generator to provide a reference while the other was moved insteps of 0.1 m in the vicinity of the break point. Data from these two wavegages measured at the same time constitute station-to-station free surface elevationtime series. Fast Fourier Transform (FFT) based cross-correlationtechniques were employed to determine the time lag between each pair of thetime series. The time lag was used to compute the phase shift between the referencewave gage and that at various points along the flume. Phase differencesbetween two points spaced 0.1 m apart were used to calculate local mean wavephase velocity for a point that lies in the middle. Results show that movingfrom deep water to shallow water, the measured mean phase velocity decreasesalmost 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 maximumvalue of 1.87 m s observed at a position 30 cm downstream of the breakpoint. Thereafter, the phase velocity decreases, reaching a minimum of about1.30 m s.

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