Research On Characteristics Of Wave-Current And Wave-Wave Nonlinear Interactions

Ocean waves often coexist with a current in the marine environment.Wave-current interaction is a universal phenomenon in nature.In reality,most waves in the ocean are irregular.There exist interaction phenomena amongst wave components with different frequencies.The feature of these phenomena is nonlinear.Most of huge waves causing accidents to ships and offshore platforms occur almost every year,and are considered to be closely associated with nonlinear wave-current interactions and wave-wave interactions.The research approaches for nonlinear wave-current and wave-wave interactions include analytical methods,numerical methods and experi-mental means.Analytical methods are prone to reveal the mechanism of the related issues,so they are extensively employed to carry out these studies.This thesis focuses on the stable,nonlinear wave-current field in finite water depth,the mass,momentum and energy flux conservation between a wave-current coexisting field and the corresponding pure wave field plus pure current field,as well as the conservation relationship of the mass,momentum and energy fluxes of a nonlin-ear bi-chromatic wave field and two corresponding monochromatic wave trains.The main work of this thesis is as follows:The interaction of nonlinear progressive waves and a uniform current in water of finite depth is investigated analytically by means of the homotopy analysis method?HAM?.To verify the HAM solutions,experiments are conducted in the wave-current flume of The Education Ministry Key Laboratory of Hydrodynamics at Shanghai Jiao Tong University?SJTU?.It is found that the HAM solutions are in good agreement with the experimental measurements.Based on the series solutions of the validated analytical model,the influence of water depth,wave steepness and current velocity on the physical properties of the coexisting wave-current field are studied in detail.The varying mechanisms of wave characteristics due to wave-current interaction are further discussed in a quantitative manner.The interaction of a current-free nonlinear wave field and a wave-free uniform current field based on a mass,momentum and energy flux conservation theory is in-vestigated in the framework of HAM.The co-existing wave-current field is assumed to be obtained by the nonlinear interaction between the current-free wave field and the wave-free current field.The equations for the mass,momentum and energy fluxes based on the accurate high-order homotopy series solutions are obtained using a dis-crete integration and a Fourier series-based fitting.The conservation equations for the mean rates of the mass,momentum and energy fluxes before and after the interaction are utilized to establish the relationship between the combined wave-current field and the current-free wave field plus the wave-free current field.The parametric analysis on nonlinearity of the waves???and current velocity?U?of the combined wave-current field respectively,is performed to obtain a standard deviation S_d,which is applied to describe the deviation from the conservation state?S_d=0?after the interaction.It is found that equal-standard deviation contours,which include very good conservation states with sufficiently small values for S_d??0.005?,can be obtained in terms of the conservation equations for the mean rates of the mass,momentum and energy fluxes before and after the interaction.A fully nonlinear solution for bi-chromatic progressive waves in water of finite depth in the framework of HAM is derived.The bi-chromatic wave field is assumed to be obtained by the nonlinear interaction of two monochromatic wave trains that prop-agate independently in the same direction before encountering.The equations for the mass,momentum and energy fluxes based on the accurate high-order homotopy series solutions are obtained using a discrete integration and a Fourier series-based fitting.The conservation equations for the mean rates of the mass,momentum and energy fluxes before and after the interaction of the two nonlinear monochromatic wave trains are proposed to establish the relationship between the steady-state bi-chromatic wave field and the two nonlinear monochromatic wave trains.The parametric analysis on?₁and?₂,representing the nonlinearity of the bi-chromatic wave field,is performed to obtain a sufficiently small standard deviation S_d,which is applied to describe the deviation from the conservation state?S_d=0?in terms of the mean rates of the mass,momentum and energy fluxes before and after the interaction.It is demonstrated that very small standard deviation from the conservation state can be achieved.After the interaction,the amplitude of the primary wave with a lower circular frequency is found to decrease;while the one with a higher circular frequency is found to increase.More-over,the highest horizontal velocity of the water particles underneath the largest wave crest,which is obtained by the nonlinear interaction between the two monochromatic waves,is found to be significantly higher than the linear superposition value of the corresponding velocity of the two monochromatic waves.