J. Bhattacharjee

Expansion formulae in wave structure interaction problems

A large class of problems in the field of fluid–structure interaction involves higher-order boundary conditions for the governing partial differential equation and the eigenfunctions associated with these problems are not orthogonal in the usual sense. In the present study, mode-coupling relations are derived by utilizing the Fourier integral theorem for the solutions of the Laplace equation with higher-order derivatives in the boundary conditions in both the cases of a semi-infinite strip and a semi-infinite domain in two dimensions. The expansion for the velocity potential is derived in terms of the corresponding eigenfunctions of the boundary-value problem. Utilizing such an expansion of the velocity potential, the symmetric wave source potentials or the so-called Greens function for the boundary-value problem of the flexural gravity wave maker is derived. Alternatively, utilizing the integral form of the wave source potential, the expansion formulae for the velocity potentials are recovered, which justifies the completeness of the eigenfunctions involved. As an application of the wave maker problem, oblique water wave scattering caused by cracks in a floating ice-sheet is analysed in the case of infinite depth.

Wave interaction with a floating rectangular box near a vertical wall with step type bottom topography

Diffraction of water waves by a floating structure near a wall with step type bottom topography is investigated under the two-dimensional small amplitude wave theory. Full solution of the problem under the potential flow approach is obtained by using the matched eigenfunction expansion method. The wave-induced forces on the structure and on the wall are studied for different water depth ratios, dimension of the structure and the distance of the wall from the structure.

Scattering of Surface and Internal Waves by Rectangular Dikes

The scattering of surface and internal waves by a single dike or a pair of identical dikes in a two-layer fluid is analyzed in two dimensions within the context of linearized theory of water waves. The dikes are approximated as cylinders of rectangular geometry and are placed in a two-layer fluid of finite depth. In the study, both the cases of surface-piercing and bottom-standing dikes are considered. The solution of the associated boundary value problem is derived by a matched eigenfunction expansion method. Because of the flow discontinuity at the interface, the eigenfunctions involved have an integrable singularity at the interface and the orthonormal relation used in the present analysis is a generalization of the classical one corresponding to a single-layer fluid. The reflection coefficients and force amplitudes are computed and analyzed in various cases. The computed results in a two-layer fluid are compared with those existing in the literature for a single-layer fluid. The results obtained by the matched eigenfunction expansion method are compared with that of wide-spacing approximation method, and it is observed that the results from both the methods are in good agreement when the dikes are widely spaced. The general behavior of reflection coefficients for interface-piercing and non-interface-piercing obstacles is found to be different in both cases of surface-piercing and bottom-standing dikes. Moreover, for surface-piercing dikes, the results show the possibility of very large resonant motions between the dikes but with a very narrow bandwidth for the frequency of interest. DOI: 10.1115/1.2786473 Floating and submerged structures are generally used to reduce the transmitted wave height and protect various types of coastal structures from a high wave attack in the downstream of wave motion. In recent years, there is a significant interest in the use of partial breakwaters to attenuate the wave energy. Most of these breakwaters are extended from the bottom up to the water surface, while partial breakwaters only occupy a segment of the whole water depth. In coastal engineering, partial barriers as breakwaters are more economical and sometimes more appropriate for engineering applications. These kinds of breakwaters also provide a less expensive means to protect beaches exposed to waves of small or moderate amplitudes and to reduce the wave amplitude at resonance. A bottom-standing partial breakwater not only resists the wave propagation but also allows the navigation of vessels over it. The bottom-standing breakwaters are being used for fish farming in coastal fishery. These breakwaters create a calm region in the downstream of the wave motion and act as a sheltered region for a large group of marine habitats during severe wave conditions. Moreover, with the environmental concerns, the bottom-standing breakwater resists the sediment transport and provides a strong protection against coastal erosion. On the other

Numerical Modelling of a Heaving Point Absorber in Front of a Vertical Wall

The hydrodynamic performance of a heaving point absorber as a wave energy converter near a large body is studied through numerical modeling. First the study is performed for an individual point absorber in the absence of large structure and the results are compared with the results available in the literature. Next, the performance of a point absorber floating in the vicinity of a large body, which is considered as a fixed vertical wall, is investigated. The efficiency of the power absorption in regular and irregular seas is examined based on different floater sizes, floater shapes, drafts, wave heading angle and positioning of the floater. Numerical simulations are based on hydrodynamic forces and coefficients, obtained with the commercial software WAMIT.Copyright

Analytical and Numerical Study of Nearshore Multiple Oscillating Water Columns

In the present study, the performance of two chamber nearshore oscillating water columns (OWCs) in finite water depth is analyzed based on the linearized water wave theory in the two dimensional Cartesian coordinate systems. The barriers are assumed to be fixed and the turbine characteristics are assumed linear with respect to the fluctuations of volume flux and pressure inside the chamber. The free surface inside the chambers is modeled as a non-plane wave surface. Two different mathematical models are employed to solve the hydrodynamic problem; the semi-analytic method of matched eigenfunction expansion and the numerical scheme of Boundary Integral Equation Method (BIEM). The numerical results are compared with the semi-analytic results and show good agreement. The effects of the distance between the barriers and the length of the barriers on the efficiency of the OWC device are investigated. The results of two chambers OWC are also compared with the results for an equivalent single OWC chamber. Further, the effect of the water depth on the capacity of the wave power absorption is discussed.© 2013 ASME

Effect of Current on Flexural Gravity Waves

The effect of uniform current on the propagation of flexural gravity waves due to a floating ice sheet is analyzed in two dimensions. The problem is formulated as an initial boundary value problem in the linearized theory of water waves. By using Laplace transform technique, the initial boundary value problem is reduced to a boundary value problem, which is solved by the application of Fourier transform to obtain the surface elevation in terms of an integral, which is evaluated asymptotically for large distance and time by the application of method of stationary phase to obtain the far field behavior of the progressive waves. The effect of current on the wavelength, phase velocity and group velocity of the flexural gravity waves propagating below the floating ice sheet is analyzed theoretically to obtain certain critical values on the speed of current which are of significant importance. Simple numerical computations are performed to observe the effect of uniform current on the surface elevation, wavelength, phase velocity and group velocity of flexural gravity waves and on the far field behavior of the progressive waves.Copyright

Wave Interaction with Floating and Submerged Rectangular Dykes in a Two-layer Fluid

In recent years, there is a significant interest in the use of partial breakwaters to control waves. Most of these breakwaters are extended from the bottom up to the water surface, while partial breakwaters only occupy a segment of the whole water depth. In coastal engineering, partial barriers as breakwaters are more economical and sometimes more appropriate for engineering applications. These kinds of breakwaters also provide a less expensive means to protect beaches exposed to waves of small or moderate amplitudes, and to reduce the wave amplitude at resonance. A bottom-standing partial breakwater not only resists the wave propagation but also allows the navigation of vessels over it. The bottom-standing breakwaters are being used for fish farming in coastal fishery. In addition, these breakwaters create a calm region in the downstream of the wave motion and act as a sheltered region for a large group of marine habitats during severe wave conditions. Moreover, with the environmental concerns, the bottom-standing breakwater resists the sediment transport and provides a strong protection against coastal erosion. On the other hand, a surface-piercing breakwater does not require a strong bottom foundation and most suitable for protecting coastal and offshore structures in deep water region. The problems of propagation of water waves by floating/submerged obstacles have been studied theoretically by many investigators within the framework of linearized potential theory in a fluid domain of constant density.