Study On The Radiation Stress Of Waves Over Two-dimensional Variable Bathymetry

In the study of nearshore wave,both the question of wave set-up on the coral reef and the resonance caused by low frequency wave on a reef flat are important to coastal engineering construction.The theory of radiation stress can explain the wave set-up,wave set-down and coastal wave-induced current well.And it's also the driving force and important influencing factor of low frequency wave.The purpose of this paper is to explore the wave motion and generation of low frequency waves.It is difficult for theoretical analysis and most numerical methods to obtain the quite accurate distribution of velocity field and pressure field,which makes it tough to calculate the radiation stress.CFD software OpenFOAM is used to simulate the waves,investigate the variation of radiation stress and the wave set-up along the shore waves.In this paper,it verifies the accuracy of the calculation method of radiation stress of First-order Stokes waves.Furthermore,the variation of regular wave radiation stress and wave set-up on the submerged bars,the slope and the coral reef are calculated.The results show that the numerical model an be used to calculate the values of wave radiation stress in the complete numerical tank.When the wave propagates on the nearshore terrain,the value of radiation stress is nearly stable at the flat topography.At the slope,it's value increases firstly then decreases after wave breaking.Besides,the value of radiation stress is sensitive to the change of amplitude,and the effect of it along the way on the wave mean water level is in good agreement with the wave set-up and set-down equation.Then,it is found the the radiation stress value of bicromatic wave changes greatly at the flat bottom,which means that the mean water lever changes and there is bound long wave.The influence of bicromatic wave radiation stress on the wave set-up can also satisfy the equation of wave set-up.And the inflection point of wave set-up lags the inflection point of wave radiation stress.In addition to,the change of wave height of wave mean square,the energy distribution and the generation of low-frequency wave of bichromatic wave and irregular wave are analyzed by the physical model experiment about wave propagation on coral reef topography.According to the experimental data,the smaller the difference frequency of bichromatic wave is,the more concentrated the energy of the main frequency is,the more intense of the speed of energy transfer and dissipation after the wave is broken,the low-frequency wave is more obvious.With the same wave height,the larger the period is,the faster the wave energy transfer speed is,and the more uniform the energy distribution on the reef flat is.The nonlinear action of the wave on the Fore-reef slope leads to the appearance of the low-frequency wave,and it released and continues to propagate on the reef flat after the wave is broken.