Multi-directional focused wave group interactions with a plane beach

Abstract

Numerical simulations and laboratory measurements are presented of multi-directional focused wave groups interacting with a plane beach. The numerical model is a two-dimensional-horizontal (2DH) hybrid flow solver, governed by a Boussinesq equation set with enhanced dispersion characteristics pre-breaking, and the nonlinear shallow water equations post-breaking. Waves are introduced into the model via an in-built multi-element piston wavemaker, allowing for complete reproduction of laboratory experiments. A wetting and drying algorithm models shoreline movement in both cross-shore and longshore directions. Predicted free surface motions of the multi-directional focused wave groups are in good agreement with wave gauge data from laboratory experiments previously carried out at the UK Coastal Research Facility (UKCRF) using a linear paddle wave generator. Both phase decomposition into Stokes-like harmonic components and wavelets provide insight into nonlinear interactions as the wave groups propagate up the beach. Free second-order error waves in a multi-directional wave group are smaller than for the corresponding uni-directional case, and spread laterally around the incoming wave group. Of the free error waves generated by linear paddle signals, only the low-frequency second-order error wave affects extreme run-up on the beach. By applying a second-order correction to the paddle signals used to generate a multi-directional wave group, it is shown that, whereas the long error wave causes a significant increase in the maximum run-up, the impact is not as severe as for the uni-directional analogue. Shoaling and run-up of the bound long waves in a spread sea are studied. Examination of the transverse structure of these subharmonic components reveals that sideways spreading in the inner surf zone contributes to reduced run-up in directionally spread groups.