Time Domain Simulation Of Wave Interaction With Structures In Two-layer Fluid

In the real ocean, density of sea water changes due to the variations in temperature and salinity in the water depth direction. In such stratified oceans, frequent internal wave gives great threat to the operation and safety of offshore structures. Therefore, the study of the action between waves and structures in the stratified oceans is not only academically important, but also is of considerable importance in practical engineering application.Based on the potential flow theory, a mathematical model with respect to the interaction between waves and arbitrary3D structures in two-layer fluids was founded by the high-order boundary element method. The model satisfies the3D Laplace equation in the upper and lower domain and satisfies the dynamic and kinematic boundary conditions in the surface and interface. Take advantage of perturbation expansion and the separation of the incident and scattering waves, a boundary value problem was established. By applying the Rankine source and its image on the seabed as the Green function in the upper and lower domain, the boundary integral equations in the upper and lower domain can be obtained through the using of the second Green identity.Through the construction of a function cp by velocity potentials of upper and lower velocity potentials on the internal surface, a single set of linear equations are set up and the amount of calculation was reduced.A fourth-order Runge-Kutta method is adopted to update the time histories of wave forces and wave profiles in the computational domain. To ensure the calculation is stable in a limited computing domain, an artificial damping layer is adopted both on the free surface and interface to avoid the wave reflection and a ramping function is used.The diffraction of structures in the two-layer fluid due to the internal mode wave was firstly derived. The exciting force on the body was computed. The results have a good agreement with the analytical method and demonstrate the effectiveness of this mathematical model. The effects of the density ratio and the depth ratio on the exciting force are discussed. It demonstrates the wave force is bigger when density ratio or depth ratio is smaller. The lower depth has a great effect on the hydrodynamics of structure when the frequency of incident wave is low. The exciting force of four cylinder structure was also computed. Second, for small amplitude force motion problems in two-layer fluid, numerical results of wave force or force moment are presented for a floating truncated cylinder by the surge and pitch motion. The computational method for added mass and damping coefficients of internal-wave mode are given. The results are compared with the analytical method and the condition of single-layer. It demonstrate the change of the fluid density have a great effect on the hydrodynamics of offshore structures in a certain frequency range.Last, combining the diffraction and radiation theory, the interaction between a free structure and the internal wave in the two-layer fluid is analyzed. The motion response and hydrodynamic forces of a truncated cylinder and four cylinders due to internal wave was presented.