Contravariant Boussinesq equations for the simulation of wave transformation, breaking and run-up

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 near shore currents in computational domains representing the complex morphology of real coastal regions. 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; 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 applied on a real case regarding the simulation of wave fields and nearshore currents in the coastal region opposite Pescara harbour (Italy)

A 3D unstructured grid nearshore hydrodynamic model based on the vortex force formalism

Acknowledgments This work was partly supported by joint Engineering and Physical Science Research Council (EPSRC) UK and Technology Foundation STW Netherlands funded SINBAD (EP/J005541/1) project. P. Zheng was supported by the China Scholarship Council during his four-year PhD study at the University of Liverpool. We would like to thank Prof. C.S. Chen of the University of Massachusetts-Dartmouth for providing the source code of FVCOM and also the SWAN developers for developing and providing this open source code. We would also like to thank the staff and personnel involved in collecting and maintaining the DUCK’94 experiment dataset and the anonymous reviewers for their constructive comments and suggestions. Computational support was provided by the Chadwick High Performance Computer at University of Liverpool and also the facilities of N8 HPC Centre of Excellence, provided and funded by the N8 consortium and EPSRC (EP/K000225/1).Peer reviewedPublisher PD

Modeling bed evolution using weakly coupled phase-resolving wave model and wave-averaged sediment transport model

In this paper, we propose a model for the simulation of the bed evolution dynamics in coastal regions characterized by articulated morphologies. An integral form of the fully nonlinear Boussinesq equations in contravariant formulation, in which Christoffel symbols are absent, is proposed in order to simulate hydrodynamic fields from deep water up to just seaward of the surf zones. Breaking wave propagation in the surf zone is simulated by integrating the nonlinear shallow water equations with a high-order shock-capturing scheme. The near-bed instantaneous flow velocity and the intra-wave hydrodynamic quantities are calculated by the momentum equation integrated over the turbulent boundary layer. The bed evolution dynamics is calculated starting from the contravariant formulation of the advection-diffusion equation for the suspended sediment concentration in which the advective sediment transport terms are formulated according to a quasi-three-dimensional approach, and taking into account the contribution given by the spatial variation of the bed load transport. The model is validated against several tests by comparing numerical results with experimental data. The ability of the proposed model to represent the sediment transport phenomena in a morphologically articulated coastal region is verified by numerically simulating the long-term bed evolution in the coastal region opposite Pescara harbor (in Italy) and comparing numerical results with the field data

Wave spectra of a shoaling wave field: A comparison of experimental and simulated results

Wave profile measurements made from an aircraft crossing the North Carolina continental shelf after passage of Tropical Storm Amy in 1975 are used to compute a series of wave energy spectra for comparison with simulated spectra. Results indicate that the observed wave field experiences refraction and shoaling effects causing statistically significant changes in the spectral density levels. A modeling technique is used to simulate the spectral density levels. Total energy levels of the simulated spectra are within 20 percent of those of the observed wave field. The results represent a successful attempt to theoretically simulate, at oceanic scales, the decay of a wave field which contains significant wave energies from deepwater through shoaling conditions