Correct generation of the bound set-down for surface gravity wave groups in laboratory experiments of intermediate to shallow depth
William Mortimer, Alison Raby, Alessandro Antonini, Deborah Greaves, Ton S. van den Bremer
Abstract
Using linear (first-order) wave generation theory in laboratory experiments, leads to significant contamination of the wave field by free non-linear (second-order) error waves, increasingly so at shallower depths. Second-order wave generation theory has previously been established, and so has correct generation of the bound set-down, made up from second-order bound waves in the sub-harmonic part of the spectrum, for bichromatic and irregular wave fields in shallow to intermediate depth. In the present work, different from previous studies, we validate second-order wave theory explicitly for isolated wave groups, which provide a demanding test on the correct generation of sub-harmonic bound waves and the stroke length of the wavemaker. We do so for shallow to intermediate water depth, where some previous attempts at full elimination of sub-harmonic error waves have been hampered by limited paddle stroke. We overcome these limitations by applying second-order wavemaker theory to a piston-type paddle with an extended paddle stroke that can thence generate the bound set-down correctly. We show that sub-harmonic error waves are eliminated by considering wave groups in relative depths k0d = 0.6–1.1, with important applications in coastal engineering experiments, such as run-up and overtopping.