A comparison between Boussinesq and NSW theories for the numerical simulation of wave setup.

Mostafa Shahrabi, Peyman Badiei, Khosrow Bargi

Monday 29 june 2015

17:42 - 17:45h at Amazon (level 1)

Themes: (T) Water engineering, (ST) River and coastal engineering, Poster pitches

Parallel session: Poster pitch: 3C. Coastal Engineering

Increase in mean water level or setup is the result of the transfer of momentum to water column during the wave breaking process. During the wave breaking process, wave energy dissipates mainly due to the turbulence. On the contrary of momentum flux continues with no dissipation. Since the momentum flux at the shoreline is zero, an increase in the mean water level occurs to compensate for the force generated by this flux and an equilibrium condition is satisfied. Considering the horizontal balance of the net wave induced stresses: radiation stresses, mean surface level changes could be obtained. So the accurate calculation of wave setup depends on the precise definition of the radiation stresses as a function of wave properties such as shape and height. Wave parameters which are employed to calculate radiation stress are functions of the applied wave theory. Stokes, Boussinesq and Nonlinear Shallow Water theories are among the nonlinear wave theories that are employed to model wave setup. Fundamentally Stokes theory is unsuitable for modeling long wave behavior on the continental shelf and coastal shallow water regions. One of the other wave theories employed in shallow water and coastal regions is the Nonlinear Shallow Water (NSW) wave theory. This theory is derived by assuming the hydrostatic pressure distribution or the uniform horizontal velocity distribution in depth. NSW equations are the basis of time dependant models which largely consider the nonlinear wave properties in shallow water regions. The Boussinesq wave theory which is based on the long wave theory, have also been used in the shallow water region. The main alternative of NSW model in predicting the wave behavior within the surf zone is Boussinesq model. The chief advantage of Boussinesq model to NSW model is the extra term of vertical acceleration. On the contrary to NSW theory, in Boussinesq theory the linear horizontal velocity distribution in depth is considered. Aim of this paper is considering Boussinesq and NSW theories capability in modeling wave setup and makes a comparison between them to propose the best theory for the numerical simulation of wave setup.