Interaction of wave with a body floating on a wide polynya

A method based on wide spacing approximation is proposed for the interaction of water wave with a body floating on a polynya. The ice sheet is modelled as an elastic plate and fluid flow is described by the velocity potential theory. The solution procedure is constructed based on the assumption that when the distance between two disturbances to the free surface is sufficiently large, the interactions between them involve only the travelling waves caused by the disturbances and the effect of the evanescent waves is ignored. The solution for the problem can then be obtained from those for a floating body without an ice sheet and for an ice sheet/free surface without a floating body. Both latter solutions have already been found previously and therefore there will be no additional effort in solution once the wide spacing approximation formulation is derived. Extensive numerical results are provided to show that the method is very accurate compared with the exact solution. The obtained formulations are then used to provide some insightful explanations for the physics of flow behaviour, as well as the mechanism for the highly oscillatory features of the hydrodynamic force and body motion. Some explicit equations are derived to show zero reflection by the polynya and peaks and troughs of the force and excited body motion. It is revealed that some of the peaks of the body motion are due to resonance while others are due to the wave characters in the polynya

Wave diffraction by a circular crack in an ice sheet floating on water of finite depth

The problem of wave diffraction by a circular crack in an ice sheet floating on water of finite depth is considered. The fluid flow is described by the linear velocity potential theory, while the infinitely extended ice sheet is modeled as a thin elastic plate with uniform properties. At the crack, zero bending moment and shear force conditions are enforced. The solution starts from the Green function for ice sheet without the crack. This is then used to obtain an integral equation, in which the jumps of the displacement and slope across the crack are the unknowns. For a circular crack, the unknowns are expanded into the Fourier series in the circumferential direction. Through imposing the boundary conditions at the crack, a matrix equation is obtained for the unknowns, which is then truncated and solved. Convergence study is undertaken with respect to the truncation, and it has been found that the series converges fast. A far field identity is used to verify the solution procedure and is found to be satisfied very accurately. Extensive results are provided, and their physical implications are discussed. These include the jumps of the displacement and slope across the crack, resonant motion, far field diffracted wave amplitude, and the deflection of the ice sheet

Motion of a floating body in a harbour by domain decomposition method

A three-dimensional domain decomposition method is used to solve the problem of wave interaction with a ship floating inside a harbour with arbitrary shape. The linearized velocity potential theory is adopted. The total fluid domain is divided into two sub-ones: one for the harbour and the other for the external open sea. Boundary integral equations together with the free surface Green function are used in the both domains. Matching conditions are imposed on the interface of the two sub-domains to ensure the velocity and pressure continuity. The advantage of the domain decomposition method over the single domain method is that it removes the coastal surface from the boundary integral equation. This subsequently removes the need for elements on the coastal wall when the equation is discretized. The accuracy of the method is demonstrated through convergence study and through the comparison with the published data. Extensive results through the hydrodynamic coefficients, wave exciting forces and ship motions are provided. Highly oscillatory behaviour is observed and its mechanism is discussed. Finally, the effects of incident wave direction, ship location as well as the harbour topography are investigated in detail

Flexural-gravity wave interaction with multiple vertical cylinders of arbitrary cross section frozen in an ice sheet

The interaction problem of flexural-gravity wave with multiple vertical cylinders frozen in an ice sheet on the surface of water with finite water depth is considered. The linearized velocity potential theory is adopted for fluid flow, and the thin elastic plate model is applied for ice sheet deflection. Each cylinder is bottom-mounted, and the shape of its cross section can be arbitrary while remaining constant in the vertical direction. The velocity potential is expanded into an eigenfunction series in the vertical direction, which satisfies the boundary condition on the ice sheet automatically. The horizontal modes, which satisfy the Helmholtz equations, are then transformed into a series of boundary integral equations along the ice sheet edges or the intersection of the ice sheet with the cylinders. The problem is then solved numerically by imposing the ice sheet edge condition together with the impermeable condition on the cylinders. The solution is exact in the sense that the error is only due to numerical discretization and truncation. Computations are first carried out for single and multiple vertical circular cylinders, and good agreements are obtained with the semi-analytical solution. To resolve the difficulty of excessive computation at a large number of cylinders, the effect of the evanescent wave of a cylinder on those at large distance is ignored. This allows for the case of a large number of cylinders in different arrangements to be simulated. Extensive results are provided. Their physics and practical relevance are discussed

Interaction of ocean wave with a harbor covered by an ice sheet

A domain decomposition method is developed to solve the problem of wave motion inside a harbor with its surface covered by an ice sheet. The shape of the horizontal plane of the harbor can be arbitrary while the sidewall is vertical. The entrance of the harbor is open to the sea with a free surface. The linearized velocity potential theory is adopted for fluid flow, and the thin elastic plate model is applied for the ice sheet. The domain is divided into two subdomains. Inside the harbor, the velocity potential is expanded into a series of eigenfunctions in the vertical direction. The orthogonal inner product is adopted to impose the impermeable condition on the harbor wall, together with the edge conditions on the intersection of the harbor wall and the ice sheet. In the open sea outside of the harbor, through the modified Green function, the velocity potential is written in terms of an integral equation over the surface of the harbor entrance, or the interface between the two subdomains. On the interface, the orthogonal inner product is also applied to impose the continuity conditions of velocity and pressure as well as the free ice edge conditions. Computations are first carried out for a rectangular harbor without the ice sheet to verify the methodology, and then extensive results and discussions are provided for a harbor of a more general shape covered by an ice sheet with different thicknesses and under different incident wave angles

Wave motions due to a point source pulsating and advancing at forward speed parallel to a semi-infinite ice sheet

The Green function, or the wave motion due to a point source pulsating and advancing at constant forward speed along a semi-infinite ice sheet in finite water depth is investigated, based on the linear velocity potential theory for fluid flow and thin elastic plate model for the ice sheet. The result is highly relevant to the ship motions near marginal seas. The ice edge is assumed to be free, or zero bending moment and shear-force conditions are used, while other edge conditions can be similarly considered. The Green function G is derived first through the Fourier transform along the direction of forward speed and then by the Wiener-Hopf technique along the transverse direction across both the free surface and ice sheet. The result shows that in the ice-covered domain, G can be decomposed into three parts. The first one is that upper ocean surface is fully covered by an ice sheet, and the second and third ones are due to the free surface and ice edge. Similarly, in the free-surface domain, G contains the component corresponding to that the upper water surface is fully free, while the second and third ones are due to the ice sheet and ice edge. In both domains, the latter two are due to the interactions of the free-surface wave and ice sheet deflection, which leads to the major complication. In-depth investigations are made for each part of G, and aim to shed some light on the nature of the wave motions induced by a ship advancing along a semi-infinite ice sheet at constant forward speed

Interaction of waves with a body floating on polynya between two semi-infinite ice sheets

The interaction of waves with a two-dimensional body floating on polynya between two semi-infinite ice sheets is investigated, based on a hybrid method utilizing a simple source function and eigenfunction matching. The ice sheet is modelled as a continuous thin elastic plate with uniform properties, while the fluid flow is described by the velocity potential. In the polynya, an integral equation is established by using the simple source function. In the two exterior ice covered regions, the potential is expanded in terms of eigenfunctions which satisfy the governing equation and all boundary conditions apart from that on the interface with the inner region. The unknown coefficients in the expansion and the boundary integral equation in the inner region are solved together by enforcing the continuity conditions of the pressure and normal velocity on the interface. The effectiveness and accuracy of the hybrid method is demonstrated through comparison with published results for a submerged cylinder and a floating rectangular body. Simulations are then carried out for a floating elliptical cylinder. Extensive results for the hydrodynamic force and motion response are provided, and the effects of ice draught as well as the body shape are investigated

Interaction of wave with multiple wide polynyas

A method based on the wide spacing approximation is applied to the wave scattering problem in multiple polynyas. An ice sheet is modeled as an elastic plate, and fluid flow is described by the velocity potential theory. The solution procedure is constructed based on the assumption that the ice sheet length is much larger than the wavelength. For each polynya, of free surface with an ice sheet on each side, the problem is solved exactly within the framework of the linearized velocity potential theory. This is then matched with the solution from neighboring polynyas at their interfaces below the ice sheet on each side, and only the traveling waves are included in the matching. Numerical results are provided to show that the method is very accurate and highly efficient. Extensive simulations are then carried out to investigate the effects of the ice sheet number, ice sheet length, distribution of ice sheets, as well as polynya width. The features of wave reflection and transmission are analyzed, and the physical mechanism is discussed

Communities as Well Separated Subgraphs With Cohesive Cores: Identification of Core-Periphery Structures in Link Communities

Communities in networks are commonly considered as highly cohesive subgraphs which are well separated from the rest of the network. However, cohesion and separation often cannot be maximized at the same time, which is why a compromise is sought by some methods. When a compromise is not suitable for the problem to be solved it might be advantageous to separate the two criteria. In this paper, we explore such an approach by defining communities as well separated subgraphs which can have one or more cohesive cores surrounded by peripheries. We apply this idea to link communities and present an algorithm for constructing hierarchical core-periphery structures in link communities and first test results.Comment: 12 pages, 2 figures, submitted version of a paper accepted for the 7th International Conference on Complex Networks and Their Applications, December 11-13, 2018, Cambridge, UK; revised version at http://141.20.126.227/~qm/papers