Short-crested waves in deep water: a numerical investigation of recent laboratory experiments

Abstract

A numerical study of quasi-steady doubly periodic monochromatic short-crested wave patterns in deep water is conducted using a high-order Boussinesq-type model. Simulations using linear wavemaker conditions in the nonlinear model are initially used to approximate conditions from recent laboratory experiments. The computed patterns share many features with those observed in wavetanks, including bending (both frontwards and backwards) of the wave crests, dipping at the crest centrelines, and a pronounced long modulation in the direction of propagation. A new and simple explanation for these features is provided, involving the release of spurious free first harmonics, due to the neglect of steady third-order components in the three-dimensional wave generation. A comparison with the experimentally observed beat length and amplitude matches the theoretical/numerical predictions well. Additionally, direct inclusion of steady third-order components in the wave generation is shown to reduce significantly the modulations (and other unsteady features), further confirming the explanation. This numerical work makes apparent some previously unknown difficulties associated with the physical generation of even the simplest three-dimensional waves, adding significant insight into the interpretation of recent experimental observations.