A new form of hyperbolic mild slope equations is derived with the inclusion of the amplitude dispersion of nonlinear waves. The effects of including the amplitude dispersion effect on the wave propagation are discussed. Wave breaking mechanism is incorporated into the present model to apply the new equations to surf zone. The equations are solved numerically for regular wave propagation over a shoal and in surf zone, and a comparison is made against measurements. It is found that the inclusion of the amplitude dispersion can also improve model's performance on prediction of wave heights around breaking point for the wave motions in surf zone.
New hyperbolic mild slope equations for random waves are developed with the inclusion of amplitude dispersion.The frequency perturbation around the peak frequency of random waves is adopted to extend the equations for regular waves to random waves.The nonlinear effect of amplitude dispersion is incorporated approximately into the model by only considering the nonlinear effect on the carrier waves of random waves,which is done by introducing a representative wave amplitude for the carrier waves.The computation time is greatly saved by the introduction of the representative wave amplitude.The extension of the present model to breaking waves is also considered in order to apply the new equations to surf zone.The model is validated for random waves propagate over a shoal and in surf zone against measurements.
The laboratory experiment and numerical simulations of wave-driven longshore currents by random waves on barred beaches with slopes of 1:100 and 1:40 were conducted to investigate the bimodal feature of mean longshore currents,with emphasis on the location and ratio of two peaks of longshore currents.The location and ratio of two peaks are controlled by the sand bar.The influences of wave heights and beach slopes on the longshore currents are discussed.Numerical simulations were also performed to compute the measured velocity profile,with the emphasis on the effect of lateral mixing,bottom friction and surface rollers on numerical results.
