Numerical Study On The Spatial Wave Focusing

When a train of plane waves enters a zone of slowly varying depth,wave energy is aggregated and wave heights increase.It is one of the generation mechanism of extreme waves.Therefore,studying the characteristics of spatial wave focusing plays an important role.In this paper,the focusing and influence factors of spatial wave focusing by two kinds of topography with curve convex slope,cones and circular truncated cone are studied in detail by means of numerical simulation based on non-hydrostatic pressure model,SWASH.By repeating previous physical experiments,we verified the accuracy of the non-hydrostatic model to simulate the wave evolution on the variable depth topography.On this basis,the focusing and influence factors of spatial wave focusing by the focusing bathymetry are discussed in detail.It is found that when the waves propagate on the curve convex slope,the wave focuses on the space,the wave heights increase and the wave nonlinearity enhances.The focusing characteristics are affected by the initial kh value,the initial kR value and the shape of the slope bathymetry contours.The smaller the kh value of the incident wave is,the stronger the nonlinear interaction of waves is,the sharper the peak is,the flatter the trough is,and the greater the probability of large wave.The initial kR is related to the deflecting velocity of the waves.The larger the initial kR is,the smaller the deflecting velocity of the waves is,and the greater the distance between the position of the maximum wave height and the toe of bathymetry.In addition,when the width of the focusing bathymetry is fixed,wave heights distribution in the focusing region are related to the shape of the slope bathymetry contours on the assumption that the slope bathymetric contours are exponential function.By comparing the propagation characteristics of regular and irregular waves,the results show that the maximum relative wave height produced by the spatial focusing of irregular waves is smaller than the maximum relative wave height of regular waves.The position of the maximum relative wave of irregular waves is generally more backward than that of regular waves.Because the wave interactions are stronger in the process of irregular wave space focusing.When irregular waves propagate on cones and circular truncated cone,waves refract.Behind the shoal topography,space focusing will appear,the fundamental frequency and super harmonic frequency enhance in the same time,and the relative wave height increases obviously.It is consistent with the theoretical solution of the regular wave on the circular truncated cone.Along the axis of the wave incident,with the depth of water shallower,the whole wave backward.The wave continues to propagate along with the focusing bathymetry,the wave spatial focusing enhances the nonlinear interaction of waves,and the wave skewness and kurtosis increase rapidly.The waves peak is sharp and steep,the trough is flat,and the probability of high waves increases.By comparing the effects of different shoal sizes and different incident wave steepness on wave focusing,it is found that the size of the shoal and the initial wave steepness have great influence on the size of the focusing area and the maximum value of relative wave height.The magnitude of wave space focusing region decreases with the increase of shoal size,and the maximum of relative wave height increases with the increase of shoal size.The smaller the incident wave steepness is,the smaller the magnitude of the focusing region,the greater the relative wave height.