TITLE:
Cross-Correlation of Station-to-Station Free Surface Elevation Time Series for Breaking Water Waves
AUTHORS:
Raphael Mukaro
KEYWORDS:
Turbulence, Plunging Breaker, Time Series, Cross-Correlation, Relative Phase, Phase Velocity
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.2,
February
28,
2018
ABSTRACT:
Free surface elevation time series of breaking water waves were measured in a
laboratory flume. This was done in order to analyze 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 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.