Numerical Analysis Of Nonlinear Internal Wave Model In Two-layer Fluid

This thesis is concerned with the interfacial wave of stratified fluid due to a point vortex in the upper layer liquid and in the upper layer liquid respectively,and a hydrofoil in the lower layer liquid.The two-layer fluid is assumed moving parallel to the interface at different velocities.The stratified flow is modeled based on the incompressible potential flow theory,with the nonlinear boundary conditions at the interface.For the point vortex located in the lower fluid,the point vortex located at the upper layer and the hydrofoil located at the lower layer,a fully nonlinear mathematical model is established,respectively.In the point vortex model,in both cases,the point vortex is located in the upper layer and in the lower layer,boundary integral equations are formulated for the fully nonlinear interfacial wave generated by the vortex,respectively.An integral-differential equation is formulated for the interfacial wave.The numerical model results in a set of nonlinear algebra equations,which are solved using the quasi-Newton method.The numerical results show that when the point vortex strength and the stratified flow condition are kept same,the interfacial wave amplitude for the point vortex is located in the upper layer is far less than it for the point vortex is located in the lower layer.And its amplitude ratio increases as the density of the upper layer and lower layer,but it's always less than unit.In the hydrofoil model,boundary integral equations are formulated for the fully nonlinear interfacial wave generated by the hydrofoil.An integral-differential equation is formulated for the interfacial wave.The numerical model results in a set of nonlinear algebra equations,which are solved using the quasi-Newton method.The wave profiles were analyzed in terms of the location and thickness of hydrofoil,Froude number and ratio of the densities of the two fluids.The wave profile depends on the Froude number.For the cases considered,h=1,?=0.01,?=0.5,the first troughs of wave profiles are bigger than others for F < 0.4,but have similar amplitudes to others for F ?0.4.The Kelvin-Helmholtz instability can occur when there is a large velocity difference across the interface between two fluids,in unsteady flow.As the thickness of the hydrofoil increases,the wave amplitude increases and the wavelength does not change.The wave amplitude and wavelength increase significantly with the density ratio of the upper layer to lower layer.As the dimensionless depth h increases,the wave amplitude firstly increases.When F=0.4,?=0.05,?=0.5,the wave amplitude reaches the maximum at about h = 0.4,and then decreases.In particular,the amplitude of the internal wave is much greater than that for the corresponding free surface wave.