Nearshore coastal flow processes using weighted-averaged equations

Abstract

This work uses the weighted residual method to simulate non-hydrostatic flows in ocean and coastal areas in a vertically-averaged framework. A Vertically-Averaged and Moment equations set is developed. The system is solved through a hybrid finite volume-finite difference numerical scheme to tackle the hyperbolic and elliptic parts of the equations. Data of seven challenging tests are used to evaluate the model ability to reproduce non-linearity, dispersion, wave breaking, bore propagation, sheet flow and wave reflection. The tests comprise propagation of sinusoidal waves over a submerged bar; convergence of the numerical scheme; solitary wave transformation over a dry reef flat, a wet reef flat and an exposed reef crest; collision of two solitary waves; and solitary wave reflection on a vertical wall under non-breaking and breaking conditions. The results highlight the accuracy of the model without prescribing any treatment for wave breaking. The conjunction of long and short waves with wave shoaling, run-up and receding flows is accurately reproduced. The model is considered an alternative tool to Boussinesq-type models to solve non-linear flows in the nearshore region, with the advantage of having an automatic mimic of wave breaking due to the field variables used to produce the weighted residual depth-averaged equations.