Numerical Analysis Of Wave Scattering And Hydrodynamic Force Acting On Floating Body In Polar Region

With the global warming of the whole planet and the melting of the Arctic ice,there has been increasing interest on topic of the Arctic routes,either for commercial,military or political use.However,when a ship sailing or other structure floating in the Arctic region,highly complex interaction between wave,ice and the structure will occur,which are much different from that in the open with free-surface domain.When the wave propagating into the complex ice/structure region,the dispersion relationship will change.And the wave energy will be partially reflected,which will enforce highly oscillations of body motion,affecting the safety of the ship as well as the harbour itself seriously.In fact,due to the complex polar terrain and changeable climate,ships will suffer from a variety of polar flow fields.Based on the domain decomposition method,complexed mathematical derivation and numerical simulation of the velocity potential solutions for wave interaction with two dimensional single polynya and multiple polynya,three diemensional non-frozen harbour and frozen harbour are respectively carried out in this paper,aiming at providing effective methodologies and valuable hydrodynamic datas for polar ships and structrues.First of all,without loss generality,for the ice-water mixed flow field,based on velocity potencial theory,the Laplace equation for fluid is provided at the beginning.To solve the second order partial differential equation,all boundary conditions of the whole domain such as the free surface,beneath the sea ice,seabed,control surface at the infinity should be determined and handled well.Especially,the elastic plate theory is adopted for describing the boundary conditions beneath the sea ice.The dispersion equations in free-surface area and ice covering area is obtained respectively by applying the separation variable method.The wave number roots of two different dispersion equations of ice water are analyzed.The procedure of solving a single free suface fluid field by boundary element method with Green function is briefly introduced.In view of the mixed boundary conditions on the free-surface and beneath the ice sheet,the necessity of domain decomposition is proposed.Secondly,for the wave/ice/body in two-dimensional single polynya,the domain decompotion is adopted for free-surface confined between two semi-infinite ice sheets and the each ice sheet on the side.Based on Green's theorem,using the ice sheet boundary equation and taking into account the two-dimensional ice edge condition,the boundary integral equation beneath the two ice sheets covered are established simultaneously.For the free surface subdomain,the boundary integral equation invloved Green's function is constructed.By considering the continuity conditons on the interface line of the subdomains,a procedure of calculating hydrodynamic force and body motion of a arbitrarily shaped structures in a two-dimensional single polynya is developed.Thirdly,for the multiple polnya,with the number of the ice sheets increasing,based on the wide space assumption,a much simper method is developed in this thesis by treating the solution of a single polynya as a basin together with the continuity on each interfaces of various subdomains.Numerical results shows a pretty high accuracy of this method.Moreover,coupled oscillation of wave reflection and transmission can be captured in calculated region.Discrate zero reflection and nearly full reflection band can be obtained in multiple polynya.For the wave/body/harbour interaction,in order to deal with the infinite bounadry integration on the coast of the harbour,the domain decomposition is proposed for dividing the whold fluid domain into inside and outside one.By introducing the three-dimensional free surface Green function,the boundary element integeral is established interior harbour.The mirror Green function and velocity potencial decomposition are introduced to avoid the integeral on infinity coastline.Thus a much simpler boundary integral equation is constructed.Based on the method introduced in this thesis,the hydrodynamic and motion mechanics of a floating body in a harbour is analyzed and the effects of the wave incident angle,the postion as well as the oritation of the ship,the uneven locally seabed and the water depth ratio of the interior and exterior harbour is investgated respectively.Finally,for the wave scattering in three-dimensional frozen harbour,the domain decompotion in free-surface harbour is reintroduced,dividing the whole complex problem into interior harbour covered with ice sheet and exterior harbour without ice sheet.The eigenfunction expansion method is implmented in the interior harbour,which transfers the Laplace equation into series of Helmhotz equations.Thus the corresponding boundary integral equation is established through Green theorem and the Green function satisfying the Helmhotz equation,that is different from the two-dimensional problem.An inner product equation is introduced in the thesis to solve the key problem of the non-orthogonality of the eigenfunction in the ice domain and the intersection boundary conditions of solid boundary of harbour and the edge of the ice sheet.By applying the continuity of the pressure and velocity on the interface,the procedure of solving the wave/ice/harbour interaction is well established.