On The Properties Of Ocean Solitary Waves With And Without Currents

The solitary wave is a common type of water waves in the ocean.Solitary waves include surface solitary waves and internal solitary waves.The water waves that propagate to coastal regions and trending to break have the same characteristics as the surface solitary waves,and the internal solitary waves appear frequently in the density-stratified oceans.The amplitude of a surface solitary wave can reach more than half of the local water depth,and the amplitude of an internal solitary wave can reach one-hundred or two-hundred meters.It is of vital importance for the design and safety assessment of the ocean structures to study the wave profile,velocity field and wave speed of the solitary waves.Furthermore,the background shear currents with complex types also exist in the oceans,and they will significantly affect the properties of the solitary waves.However,few research works focused on the properties of the surface solitary waves and the two-layer internal solitary waves in the complex-type background shear currents,and even no works considered the properties of the three-layer internal solitary waves in the complex-type background shear currents.Since the high-level Green-Naghdi water-wave theory and the high-level Green-Naghdi internal-wave theory are the strongly nonlinear,strongly dispersive wave theories and no irrotationality is introduced,the wave profile,velocity field and wave speed of the surface solitary waves,two-layer and three-layer internal solitary waves in the linear and nonlinear background shear currents are studied respectively by use of the two theories in this thesis,which will verify the influences of the background shear currents on the solitary-wave properties,and provide the reliable theoretical supports for the forces and the motion responses of the ocean structures in the complex wave-current conditions.Firstly,the governing equations and boundary conditions of the existing HLGN theory are introduced,and the linear dispersion relations of the HLGN theory with different levels are presented.By comparing with the exact linear dispersion relation,the application scopes of the HLGN theory with different levels are determined.Then,the governing equations and boundary conditions of the multi-layer(more than two layers)HLGN internal-wave theory are derived for the first time,and the linear dispersion relations of the two-layer and three-layer HLGN theories with different levels are presented respectively.By comparing with the exact linear dispersion relations,the application scopes of the two-layer and three-layer HLGN theories with different levels are determined respectively.Secondly,a numerical algorithm for the steady solution of the surface solitary waves based on the HLGN theory are introduced,and the HLGN theory is applied for investigating the properties of the surface solitary waves in the absence and presence of linear and nonlinear background shear currents for the first time.By comparing with other numerical or theoretical results,we find that the HLGN theory can describe the properties of the surface solitary waves with and without currents accurately.In addition,we find that the background shear currents affect the wave profile,velocity field and wave speed of the surface solitary waves significantly.Thirdly,a numerical algorithm for the steady solution of the internal solitary waves based on the two-layer HLGN theory are presented,and the two-layer HLGN theory is applied for investigating the properties of the internal solitary waves in a two-layer fluid system in the absence and presence of linear and nonlinear background shear currents for the first time.By comparing with other numerical or theoretical results,we find that the two-layer HLGN theory can describe the properties of the internal solitary waves in a two-layer fluid system with and without currents accurately.In addition,we find that the background shear currents affect the wave profile,velocity field and wave speed of the internal solitary waves in a two-layer fluid system significantly.Furthermore,we apply the two-layer HLGN theory for investigating the internal waves in the South China Sea.It is demonstrated that the two-layer HLGN theory can accurately describe the wave profile and velocity field of the internal solitary waves in the South China Sea.Finally,numerical algorithms for the steady solution of the internal solitary waves and time-domain simulation based on the three-layer HLGN theory are presented,and the three-layer HLGN theory is applied for investigating the properties of the internal solitary waves in a three-layer fluid system in the absence and presence of linear and nonlinear background shear currents for the first time.For the no-current cases,the effects of the pycnocline on the properties of the internal solitary waves are analyzed.By comparing with the results of the two-layer HLGN theory which ignore the pycnocline effects,we find that the pycnocline has great influences on the velocity field and wave speed of the internal solitary waves.For the linear and nonlinear background shear-current cases,we study the wave profile,velocity field and speed affected by the background shear currents by fixing the amplitude of the internal solitary wave between the upper-fluid layer and the middle-fluid layer.Results show that the background shear currents not only affect the wave profile of the internal solitary wave between the upper-fluid layer and the middle-fluid layer,but also affect the amplitude of the internal solitary wave between the middle-fluid layer and the lower-fluid layer.Furthermore,the background shear currents affect the velocity field and wave speed of the internal solitary waves in a three-layer fluid system significantly.At last,we apply the three-layer HLGN theory for investigating the internal waves in the South China Sea and find that the three-layer HLGN theory can accurately describe the wave profiles of the mode-1 and mode-2 internal solitary waves in the South China Sea.