In this paper we propose an integral form of the fully non-linear Boussinesq equations in contravariant formulation, in which Christoffel symbols are avoided, in order to simulate wave transformation phenomena, wave breaking and nearshore currents in computational domains representing the complex morphology of real coastal regions. Following the approach proposed by Chen (2006), the motion equations retain the term related to the approximation to the second order of the vertical vorticity. A new Upwind Weighted Essentially Non-Oscillatory scheme for the solution of the fully non-linear Boussinesq equations on generalised curvilinear coordinate systems is proposed. The equations are rearranged in order to solve them by a high resolution hybrid finite volume-finite difference scheme. The conservative part of the above-mentioned equations, consisting of the convective terms and the terms related to the free surface elevation, is discretised by a high-order shock-capturing finite volume scheme in which an exact Riemann solver is involved; dispersive terms and the term related to the approximation to the second order of the vertical vorticity are discretised by a cell-centred finite difference scheme. The shock-capturing method makes it possible to intrinsically model the wave breaking, therefore no additional terms are needed to take into account the breaking related energy dissipation in the surf zone. The model is verified against several benchmark tests, and the results are compared with experimental, theoretical and alternative numerical solutions. (C) 2013 The Authors. Published by Elsevier B.V. All rights reserved
Submerged shore-parallel breakwaters for coastal defence (henceforth SBWs) are a good compromise between the need to mitigate the effects of waves on the coast and the ambition to ensure the preservation of the landscape and water quality. However, if not properly designed, such structures can force circulation patterns that enhance shoreline erosion rather than shoreline accretion. Numerical models can be used to investigate the structure-induced circulation patterns and the resulting shoreline response. However, being computationally demanding these models are most suitable for advanced stages of the design process. The aim of this paper is to present a simple criterion to qualitatively identify whether an accretive or erosive circulation pattern can be expected in the lee of the structures. The criterion is based on analytical considerations and builds on the model presented by Bellotti (2004Bellotti ( , 2007. It is validated against the non-hydrostatic free surface numerical model SWASH (Zijlema et al. 2011) and experiments performed by . The validation indicates that the proposed analytical model is capable of providing a rapid first assessment of the potential shoreline response mode for SBW design.
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