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Godunov‐type adaptive grid model of wave–current interaction at cuspate beaches
Author(s) -
Rogers Benedict D.,
Borthwick Alistair G. L.,
Taylor Paul H.
Publication year - 2004
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.760
Subject(s) - geology , wave setup , surf zone , wave height , mechanics , turbulence modeling , bathymetry , turbulence , meteorology , geometry , physics , wave propagation , mathematics , mechanical wave , longitudinal wave , oceanography , quantum mechanics
This paper presents a second‐order accurate Godunov‐type numerical scheme for depth‐ and period‐averaged wave–current interaction. A flux Jacobian is derived for the wave conservation equations and its eigensystem determined, enabling Roe's approximate Riemann solver to be used to evaluate convective fluxes. Dynamically adaptive quadtree grids are used to focus on local hydrodynamic features, where sharp gradients occur in the flow variables. Adaptation criteria based on depth‐averaged vorticity, wave‐height gradient, wave steepness and the magnitude of velocity gradients are found to produce accurate solutions for nearshore circulation at a half‐sinusoidal beach. However, the simultaneous combination of two or more separate criteria produces numerical instability and interference unless all criteria are satisfied for mesh depletion. Simulations of wave–current interaction at a multi‐cusped beach match laboratory data from the United Kingdom Coastal Research Facility (UKCRF). A parameter study demonstrates the sensitivity of nearshore flow patterns to changes in relative cusp height, angle of wave incidence, bed roughness, offshore wave height and assumed turbulent eddy viscosity. Only a small deviation from normal wave incidence is required to initiate a meandering longshore current. Nearshore circulation patterns are highly dependent on the offshore wave height. Reduction of the assumed eddy viscosity parameter causes the primary circulation cells for normally incident waves to increase in strength whilst producing rip‐like currents cutting diagonally across the surf zone. Copyright © 2004 John Wiley & Sons, Ltd.