Numerical Study On The Nonlinear Interactions Between Bidirectional Wave Trains

Nonlinear interaction,as an important feature of ocean waves,is ubiquitous on the ocean surface.Most of the related research mainly target unidirectional progressive waves.In fact,real waves in the ocean are propagating multi-directionally and usually show obviously threedimensional characteristics,thus the study on the interactions of three-dimensional waves is more meaningful.However,up to now,the research on completely three-dimensional waves is still difficult.In this paper,the nonlinear interactions of two wave trains with specified angle are systematic studied based on a numerical “X” wave flume by fully non-hydrostatic threedimensional free surface flow model.This is not only the extension of the previous twodimensional study but also the experience and foundation for the further study of completely three-dimensional nonlinear wave interaction.By simulating the interactions of two identical wave trains,we found that the approaching angle of waves trains is highly correlated with the interaction between bidirectional regular waves.Large approaching angle can lead to intense interactions and strongly three-dimensional characteristics of the wave trains after interaction.Then the interactions of two focusing wave groups were simulated,and amplitude statistics,analysis of velocity profile,energy calculation and spectral analysis were employed to research the influence of wave steepness and approaching angle on the interaction process.The results show that larger approaching angle can lead to more intense interaction and faster energy growth,which is consistent with the results of related identical waves.The profile analysis results demonstrate that in the horizontal direction,when the wave crest has just entered the interaction region,the downward velocity of the wave peak tends to approach,and the middle velocity is greater than that of the two sides.While after the crest passes through the center of interaction region,the direction of velocity becomes separated.Along the vertical direction,for both two-dimensional(2D)and three-dimensional(3D)conditions,the wave crest tilt forward in the focusing process,and the crest-front velocity is larger than the crest-rear velocity.After focusing,the wave crest will lean back,and the crest-front velocity is less than the crest-rear velocity.Compared with 2D experiments,the 3D nonlinear wave interactions can lead to larger and steeper wave crest.In addition,the included angle also has an important influence on wave crest.The larger angle,the more severe forward or backward leaning but smaller velocity under the wave crest.The results of energy calculation indicate that under 3D condition,the potential energy and kinetic energy of whole wave groups are equal before propagating to the interaction region.However,due to the violent interactions in the interaction region,they are no longer equal but dominant alternately with propagating.Compared with the initial wave steepness,the effect of angle on the change of potential and kinetic energy is more obvious.Larger angle can lead to more intense nonlinear interactions and more remarkable concussion of potential and kinetic energy in the interaction region.The results of spectral analysis show that there is nonlinear energy transfer from basic frequency band to lower and higher frequency bands(mainly to high frequency bands)in the process of wave focusing.after the focus,the shifted energy will come back.In addition,the interactions of focusing wave groups can also lead to strongly three-dimensional characteristics of the wave trains after interaction(increase of energy in the high frequency bands),which is highly related with approaching angle and wave steepness.Lager angle and wave steepness can lead to stronger three-dimensional characteristics of the wave trains after interaction and longer propagation distance or time is needed to return the shifted energy.