Estimation of incident and reflected components in nonlinear regular waves over sloping foreshores

The present paper deals with separation of long-crested regular waves into incident and reflected components. Such methods have been available for several decades for linear waves, but has recently been extended to cover nonlinear waves over horizontal foreshores. The overall goal of the present paper is to extend the separation method for nonlinear regular waves to cover also sloping foreshores. This requires the combination of the existing method with a nonlinear shoaling model. A nonlinear shoaling model was very recently found valid for the shoaling of the primary and bound components in regular waves when the slope angle is positive and mild. In the present paper this shoaling model is utilized and assumed valid also for the de-shoaling of the reflected waves, i.e. on a negative mild slope angle. However, if the reflected waves are nonlinear the de-shoaling process is much more complicated and will for example cause release of free waves. Interactions among those free reflected wave components may cause nonlinear interactions not included in the mathematical model. For that reason, the applicability range is limited to mildly nonlinear reflected waves. Using numerical model data with various foreshore slopes, wave nonlinearities and reflection coefficients the reliability of the developed model is examined in detail.