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 nonlinearity, 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.