On the experimental measurement of wave-by-wave properties

Wave measurements from fixed gauges in a flume produce time-series of surface elevation. To characterize the waves, and enable a comparison with theory, additional spatial information is needed. This is commonly obtained by simultaneous measurements at pairs of gauges with spacing much smaller than a typical wavelength, assuming the surface profile to be frozen between the gauges. Although a “wave” can be defined as the signal between successive positive or negative zero-crossings, between successive crests, or between successive troughs, experimental measurements are not agnostic to the choice of metric. We show that wave-by-wave measurements of phase velocity or wavelength are most stable and consistent over repeated experiments when using wave-by-wave cross correlation, as opposed to the passage of zero-crossings, crests or troughs. The high variability of these other metrics may contribute to some of the difficulty in measuring nonlinear wave properties in flume experiments.