This paper describes the development of a numerical model for studying the evolution of a wave train, shoaling and breaking in the surf zone. The model solves the Reynolds equations for the mean (ensemble average) flow field and the k–e equations for the turbulent kinetic energy, k, and the turbulence dissipation rate, e. A nonlinear Reynolds stress model (Shih, Zhu & Lumley 1996) is employed to relate the Reynolds stresses and the strain rates of the mean flow. To track free-surface movements, the volume of fluid (VOF) method is employed. To ensure the accuracy of each component of the numerical model, several steps have been taken to verify numerical solutions with either analytical solutions or experimental data. For non-breaking waves, very accurate results are obtained for a solitary wave propagating over a long distance in a constant depth. Good agreement between numerical results and experimental data has also been observed for shoaling and breaking cnoidal waves on a sloping beach in terms of free-surface profiles, mean velocities, and turbulent kinetic energy. Based on the numerical results, turbulence transport mechanisms under breaking waves are discussed.

A numerical study of breaking waves in the surf zone

Mathematical and experimental modelling of sediment transport processes in the coastal environment is presented. The convectiondiffusion equation for suspended sediment particles has been used to compute the vertical distribution of the time-averaged concentrations. The computed results are compared with measured values of laboratory and field experiments (surf zone Dutch coast).

/pdf/sediment-transport-by-currents-and-waves-3bmk6oxzl5.pdf

Sediment Transport by Currents and Waves

Based on the linearized governing equations, a bottom roughness specified by the equivalent Nikuradse sand grain roughness, fcjv, and a timeinvariant eddy viscosity analogous to that of Grant and Madsen (1979 and 1986) the solution is obtained for combined wave-current turbulent bottom boundary layer flows with the wave motion specified by its near-bottom orbital velocity directional spectrum. The solution depends on an a priori unknown shear velocity, u*r, used to scale the eddy viscosity inside the wave boundary layer. Closure is achieved by requiring the spectral wavecurrent model to reduce to the Grant-Madsen model in the limit of simple periodic plane waves. To facilitate application of the spectral wave-current model it is used to define the characteristics (near-bottom orbital velocity amplitude, U(,r, radian frequency, uir, and direction of propagation, 4>wr) of a representative periodic wave which, in the context of combined wavecurrent bottom boundary layer flows, is equivalent to the wave specified by its directional spectrum. Pertinent formulas needed for application of the model are derived and their use is illustrated by outlining efficient computational procedures for the solution of wave-current interaction for typical specifications of the current

/pdf/spectral-wave-current-bottom-boundary-layer-flows-28a70zw1mw.pdf

Spectral wave-current bottom boundary layer flows

Impacts of climate change on water erosion: A review

A theoretical model is developed for wave heights and set-up in a surf zone. In the time averaged equations of energy and momentum the energy flux, radiation stress and energy dissipation are determined by simple approximations which include the surface roller in the breaker. Comparison with measurements shows good agreement. Also the transitions immediately after breaking are analysed and shown to be in accordance with the above mentioned ideas and results.

/pdf/wave-heights-and-set-up-in-a-surf-zone-39q6lqmhg5.pdf

Wave Heights and Set-up in a Surf Zone

A breaking wave propagation model based on the Boussinesq equations

Mathematical Theory of Waves Mathematical Models for Coastal Circulation Water Quality Coastal Models Mathematical Models of Sediment Transport in Coastal Areas Index.

Mathematical models in coastal engineering

Nonlinear wave transformation in the surf and swash zone is computed by a nonlinear breaking wave model based on the numerical solution of the Boussinesq-type equations. Instead of classical equations, higher-order equations in dispersion as well as in nonlinearity are derived and used inside and outside the surf zone. The Dibajnia and Watanabe transport rate formula involving unsteady aspects of the sand transport phenomenon is adopted for estimating sheet flow sediment transport rates as well as the bed load and suspended load over ripples. For the calculation of the suspended load induced by wave breaking, the Bailard formula is used after the consideration that the only dissipation mechanism is the wave breaking. Runup and rundown as well as sediment transport in the swash zone are incorporated in the model. The model is able to reproduce beach accretion and erosion without the use of an erosion/accretion criterion. The model is validated against large-scale experimental data.

Surf and Swash Zone Morphology Evolution Induced by Nonlinear Waves

A three-dimensional numerical model has been developed to study hydrodynamic circulations produced in coastal zones due to tide and wind action. The model consists of a mixed finite-difference/finite element solution of the simplified fluid momentum and continuity equations. A numerical splitting technique is used to reduce the size of model solution matrices while the finite element approach is used over the flow depth to enable irregular sea beds to be tackled easily. Model errors arising from the numerical method are minimized by the use of a Galerkin weighted-residual procedure. The problems associated with modeling the turbulence closure of the basic momentum equations are also investigated with a simplified form of the model and the need for high levels of closure is demonstrated. The potential use of the three-dimensional model is illustrated by prediction of wind-induced flows in Thessaloniki Bay in the Aegean Sea.

Modeling Three-Dimensional Wind-Induced Flows

Modeling the impact of climate change on sediment transport and morphology in coupled watershed-coast systems: A case study using an integrated approach

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