Accurate surf zone modelling is a major interest in coastal engineering; given the high computational cost of solving Navier-Stokes equations, shallow water theories – Boussinesq-type equations (BTEs) and nonlinear shallow water equations (NSWEs)– remain relevant. BTEs are the most popular, because they account for both nonlinearity and dispersion at different accuracy levels. However, Boussinesq models have a shortcoming: artificial techniques are needed to simulate shoreline motion and wave breaking. Here a new treatment of wave breaking is proposed. The 2DH Boussinesq equations of Madsen and Sørensen (1992) are solved by a FVM-FDM scheme. Wave breaking modelling is based on two considerations: (1) in shallow waters, as breaking is approached, dispersion becomes negligible compared to nonlinearity, hence, NSWEs are an appropriate approximation of the flow and can be solved instead of Boussinesq equations; (2) when integrated by shock-capturing methods, NSWEs intrinsically represent the propagation of bores, which are similar to spilling breakers. A criterion, based on such similarity and not subject to calibration, is introduced to establish when the conditions for the application of NSWEs are achieved. Once NSWEs are applied, wave breaking is automatically handled: wave height decay and mean water level setup emerge as parts of the solution. Comparisons between numerical results and experimental data show that wave breaking and its effects on the flow are accurately modelled; complexity and arbitrariness are limited with respect to traditional methodologies.
Shock capturing Boussinesq model for wave breaking simulation
PETTI, Marco;BOSA, Silvia
2010-01-01
Abstract
Accurate surf zone modelling is a major interest in coastal engineering; given the high computational cost of solving Navier-Stokes equations, shallow water theories – Boussinesq-type equations (BTEs) and nonlinear shallow water equations (NSWEs)– remain relevant. BTEs are the most popular, because they account for both nonlinearity and dispersion at different accuracy levels. However, Boussinesq models have a shortcoming: artificial techniques are needed to simulate shoreline motion and wave breaking. Here a new treatment of wave breaking is proposed. The 2DH Boussinesq equations of Madsen and Sørensen (1992) are solved by a FVM-FDM scheme. Wave breaking modelling is based on two considerations: (1) in shallow waters, as breaking is approached, dispersion becomes negligible compared to nonlinearity, hence, NSWEs are an appropriate approximation of the flow and can be solved instead of Boussinesq equations; (2) when integrated by shock-capturing methods, NSWEs intrinsically represent the propagation of bores, which are similar to spilling breakers. A criterion, based on such similarity and not subject to calibration, is introduced to establish when the conditions for the application of NSWEs are achieved. Once NSWEs are applied, wave breaking is automatically handled: wave height decay and mean water level setup emerge as parts of the solution. Comparisons between numerical results and experimental data show that wave breaking and its effects on the flow are accurately modelled; complexity and arbitrariness are limited with respect to traditional methodologies.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
