3D Full Time-Domain Numerical Models Of Simulating The Interaction Between Waves And Bodies In Shallow Water And Their Applications

As for offshore and port engineering,the waves have their own unique characteristics owing to the shallow water depth.To be more specific,in accordance with the different relations among wave height,wave length and water depth,periodic waves can be expressed as cnoidal waves or Stokes waves.At the same time,the influnce of the underwater topography and water area boundary on wave propagation is vitally important,and wave diffraction,reflection,etc.caused by them have a significant influence on the engineering.Therefore,the numerical models on the interaction between waves and bodies in shallow water should be set up to simulate the complex wave issues in offshore and port engineering.Using the numerical models,the interaction between cnoidal waves and bodies should be simulated and examined,and the effect of the wave nonlinearity on the interaction should be researched into.The established model should meet the basic requirements of three aspects:(1)It can accurately simulate various nonlinear waves in the offshore and port water areas,including cnoidal waves and Stokes waves in a certain water depth range;(2)It can accurately simulate wave propogation in a large water area over a varing underwater topography;(3)It can accurately solve the problems with curved boundaries.In view of this,on the one hand,based on the improved Boussinesq equations derived by Beji and Nadaoka,a numerical model simulating wave propagation and the interaction between waves and settled vertical stuctures in shallow water was set up.In this model,the handling method for the curved boundary was improved to accurately meet the fully reflective condition.The tests showed that this model can accurately simulate nonlinear waves and solve the problems with a large-area varing underwater topography and curved boundaries.By virtue of this model,systematic research into the run-up of cnoidal waves on a cylinder was further carried out,and the effect of dimensionless parameters on the wave run-up was examined.Especially,it was revealed that among cnoidal waves with the same Ursell number,there seemingly are the same nonlinearity due to the same normalized wave profile,however,differences in the run-up of the waves still exist owing to the differences in the relative wave height.In addition,the maximum dimensionless run-up was predicted under various conditions.On the other hand,based on the established Boussinesq equation model,the full time domain combined model was further set up to calculate the floating body motion response induced by waves in shallow water.In the present model,the Cummins method was replaced which was adopted in the similar traditional combined model.In the Cummins method,the diffraction potential and the radiation potential caused by the floating body motion are separately calculated,and then the added mass and the hysteresis function in the motion equation are calculated by means of the frequency domain results and the convolution integral in order to solve the motion equation.The present model used a full time domain method which directly calculated the scattered potential(including the diffraction potential and radiation potential)through Laplace equation and progressively calculate the time integral and solve the motion equation along with time steps.As a result,based on Boussinesq equations by which the propagation of the incident waves is simulated in the time-domain,the established combined model truly becomes a full time-domain numerical model.In order to simplify the calculation,the scattered waves are considered as linear waves in this model,just like the similar models.The tests showed that this model can effectively calculate the floating body motion response induced by nonlinear waves.Finally,by means of this combined model,the motion response of a floating box induced by cnoidal waves was calculated.The effect of the nonlinearity of the cnoidal waves on the motion was shown with tested wave trains with different wave heights and wavelengths.In short,based on the improved Boussinesq equations,two numerical models of simulating the interaction between waves and bodies in shallow water were set up in this study.One of them can accurately simulate wave propagation and the interaction between waves and settled vertical structures in the offshore and port water area;the other one can effectively calculate the motion response of the floating body induced by waves in this water area.By virtue of the two models,the interaction between cnoidal waves and bodies was carefully researched into.The effect of the nonlinearty of cnoidal waves on the interaction and the considerable differences between cnoidal waves and Stokes waves were presented.