Zhili Zou

Modelling of 2-D extended Boussinesq equations using a hybrid numerical sc-heme

In this paper, a hybrid finite-difference and finite-volume numerical scheme is developed to solve the 2-D Boussinesq equations. The governing equations are the extended version of Madsen and Sorensen’s formulations. The governing equations are firstly rearranged into a conservative form. The finite volume method with the HLLC Riemann solver is used to discretize the flux term while the remaining terms are discretized by using the finite difference method. The fourth order MUSCL-TVD scheme is employed to reconstruct the variables at the left and right states of the cell interface. The time marching is performed by using the explicit second-order MUSCL-Hancock scheme with the adaptive time step. The developed model is validated against various experimental measurements for wave propagation, breaking and runup on three dimensional bathymetries.

Competition of Class I and II Instabilities in Evolution of Crescent Waves

A laboratory experiment on the instability of Stokes wave trains with large steepness in finite water depths in a wave basin is performed. Two class instabilities of Stokes wave, quartet interaction and quintet interaction, were observed, and it is found that the evolution of crescent wave pattern is affected by the development of quintet interaction. The dependence of this effect on relative water depth was analyzed. The wave steepness for the occurrence of the competition is examined by applying linear instability analysis of Stokes wave.Copyright

Boussinesq Modelling of Nearshore Waves Under Body Fitted Coordinate

A set of nonlinear Boussinesq equations with fully nonlinearity property is solved numerically in generalized coordinates, to develop a Boussinesq-type wave model in dealing with irregular computation boundaries in complex nearshore regions and to facilitate the grid refinements in simulations. The governing equations expressed in contravariant components of velocity vectors under curvilinear coordinates are derived and a high order finite difference scheme on a staggered grid is employed for the numerical implementation. The developed model is used to simulate nearshore wave propagations under curvilinear coordinates, the numerical results are compared against analytical or experimental data with a good agreement.

Reproducing Laboratory-Scale Rip Currents on a Barred Beach by a Boussinesq Wave Model

The pioneering work of Haller [8] on physically investigating bathymetry-controlled rip currents in the laboratory is a standard benchmark test for verifying numerical nearshore circulation models. In this paper, a numerical model based on higher-order Boussinesq equations was developed to reproduce the number of experiments involved in such an investigation, with emphasis on the effect of computational domain size on the numerical results. A set of Boussinesq equations with optimum linear properties and second-order full nonlinearity were solved using a higher-order finite difference scheme. Wave breaking, moving shoreline, bottom friction, and mixing were all treated empirically. The developed model was first run to simulate the rip current under full spatial and time-domain conditions. The computed mean quantities, including wave height, mean water level, and mean current, were compared with the experimental data and favorable agreements were found. The effects of computational domain size on the computation results were then investigated by conducting numerical experiments. The Willmott index was introduced to evaluate the agreements between the computed results and data. Inter-comparisons between the computation results and measurements demonstrated that the computational domain size significantly influenced the numerical results. Thus, running a Boussinesq wave model under full spatial and time-domain conditions is recommended to reproduce Hallers experiment.

Crescent Waves on Finite Water Depth

A laboratory experiment on generation and evolution of L2-type crescent waves was performed with focus on the effects of finite water depth on crescent waves. The new results include the critical wave steepness for triggering crescent waves, the characteristics of the wave surface pattern and amplitude spectrum, and the parameters of surface elevation.Copyright