Narrow Results

A new model for nearshore nonlinear water wave is established through the Galerkin Chebyshev spectral approach on the vertical direction. The model is based on the spatial-temporal separation conception. The Galerkin Chebyshev spectral approach is applied to solve the Laplace equation, while the Zakharov's expression of the free surface boundary condition is considered as the evolution equation of the free surface and integrated temporally. The accuracy and efficiency of the model are confirmed by the results of simulation of water waves over even bottom, nonlinear wave shoaling and harmonic generation over a submerged bar. Finally, the model is used to study the wave blocking phenomenon due to strong opposing currents. Both the location of the blocking point and the wave structure near the point are well presented.

In this paper, we present a model for the amplitude evolution of periodic waves blocked by a counter current. The model consists of a WKB-solution for slowly varying waves far from the blocking point which is matched with a uniformly-valid approximation for the rapidly varying waves near the blocking point. Wave energy dissipation is taken into account both in the regions far from and near to the blocking point. The predicted pattern of wave amplitude evolution agrees well with observations.

A spectral model is presented for blocking of long-crested random waves due to nonuniform collinear adverse current in the steady state situation. The spatial evolution of the spectral components in the region far from the blocking points (far field) is modeled with a spectral wave action balance, which is matched with a uniformly-valid solution in the region near the blocking points (near field). Wave-energy dissipation is taken into account both in the far and near fields, particularly dissipation due to wave breaking. Model results are compared with experimental data for the case of partial blocking and of nominally complete blocking. The value of the onset-breaking parameter γ, which is a calibration parameter, that can best reproduce the observations in both cases is γ≈0.55. The fitted model is able to reproduce the observed patterns of the wave-height variation along the flume well and the observed variance spectra fairly well.

A set of fully nonlinear Boussinessq-type equations with improved linear and nonlinear properties is considered for wave–current interaction analysis. These phase-resolving equations are so that the highest order of the derivatives is three. We implement a new source function for the wave–current generation within the domain, which allows to generate a wide range of wave–current conditions. The set of equations is solved using a fourth order explicit numerical scheme which semi-discretizes the equations in space and then integrates in time using an explicit Runge–Kutta scheme. A novel treatment of the boundaries, which uses radiative boundary conditions for the current and damps the waves, is used to avoid boundary reflections. Several validation tests are presented to demonstrate the capabilities of the new model equations for wave–current interaction.