The study of wave-blocking and current effects on nonlinear interactions of shallow-water waves using advanced Boussinesq models

The first part of this work focuses on the derivation of enhanced Boussinesq-type equations for the combined motion of waves and currents in shallow water areas.;The strategy proposed in this work is to couple two known methods which are the sponge layer concept suitable for short waves and Sommerfeld radiation condition for currents. This coupling method provides satisfactory non-reflective boundaries for the simulation of fully coupled wave/current motion as demonstrated by the numerical experiments. We verify the model against the well known solutions based on the existing theories and good agreement has been observed. The numerical results confirm the non-breaking single-reflection process of wave blockage although the reflected waves are not well resolved by the model due to the grid size limit. With respect to the blockage of higher-harmonics generated by nonlinear shoaling, we can conclude that as long as the higher-harmonics are bound with the primary wave, they can propagate against a strong opposing current which is strong enough to block the free higher-harmonics.;To investigate the effect of the nonlinearity on the wave blockage, we derive the third-order solution of the new set of Boussinesq-type equations following the Stokes-type expansion technique and the results are compared with the target solution by Baddour & Song (1990) who derived the solution from potential theory. In the case of strong nonlinearity, the removal of wave-blocking by the amplitude effect may lead to wave breaking due to the wave steepness limit.;Current effects on nonlinear interactions of shallow-water waves are also investigated. An opposing current will diminish the extent of triad interactions while a following current will intensify energy exchange between wave components. This is in complete, direct contrast to the current effects on deep-water waves. The shoaling tests also demonstrate that an ambient current has less effect on bounded harmonics than on free harmonics.;The theoretical and numerical results obtained in the present work show that the new Boussinesq-type equations for fully coupled wave/current interaction make it possible to simulate a range of complicated phenomena related to the interaction of waves and the depth-uniform current in coastal regions. (Abstract shortened by UMI.).