Concerted nonlinear mild-slope wave models for enhanced simulation of coastal processes

Abstract

• One-way coupling of parabolic and hyperbolic models. • Introducing exact nonlinear wave effects in parabolic models. • Handling efficiently the principal wave propagation direction in parabolic models. • Models verification against demanding experiments. The present paper aims to incorporate nonlinear amplitude dispersion effects in parabolic and hyperbolic approximation models. First, an explicit and analytical method for considering nonlinearities in parabolic approximation models is investigated. This method follows the concept of calculating spatially and temporally varying wave phase celerities within the simulation. The nonlinear dispersion relation to be applied is dependent on the local Ursell number and wave steepness, in relation to valid regions of analytical wave theories. Furthermore, nonlinearities are introduced in a hyperbolic approximation model by proposing a novel method which combines a parabolic and a hyperbolic model without a significant loss in accuracy, leading to a substantial reduction in the required simulation time. This is achieved by inputting initial boundary conditions into the hyperbolic model based on the output of the parabolic model, which is used for an initial calculation of the spatial distribution of nonlinear dispersion effects over the entire numerical domain. Numerical results were compared with measurements obtained via demanding experimental setups and illustrated satisfactory performance of the models. These concerted nonlinear models offer ease in implementation, short simulation times, and accurate results while incorporating the majority of wave transformation processes including shoaling, refraction, diffraction, reflection, bottom friction and depth-induced wave breaking.