T. Sahoo - Academia.edu (original) (raw)

Papers by T. Sahoo

Zeitschrift für angewandte Mathematik und Physik, 2015

Proceedings Mathematical Sciences, 1996

Physics of Fluids, 2001

A new inner product is developed based on the Fourier analysis to study the scattering of surface... more A new inner product is developed based on the Fourier analysis to study the scattering of surface waves by a floating semi-infinite elastic plate in a two-dimensional water domain of finite depth. The eigenfunctions for the plate-covered region are orthogonal with respect to this new inner product. The problem is studied for various wave and geometrical conditions. Especially, the influence of different edge conditions on the hydrodynamic behavior is investigated and compared. The edge conditions considered in the present study involve ͑i͒ a free edge, ͑ii͒ a simply supported edge, and ͑iii͒ a built-in edge. The hydrodynamic performance of an elastic plate is characterized for various conditions in terms of wave reflection and transmission, plate deflection, and surface strain. It is observed that the hydrodynamic behavior depends on the wave conditions, the geometrical settings, and the edge conditions. The built-in edge condition induces the maximum wave reflection and the minimum wave transmission. The free edge condition leads to the maximum plate deflection.

Journal of Applied Mechanics, 2001

The wave resonance in a circular harbor surrounded by a porous seawall is analyzed. Matching the ... more The wave resonance in a circular harbor surrounded by a porous seawall is analyzed. Matching the velocity and pressure along the porous seawall and the harbor entrance, the full solution is obtained. The resonance condition is found to depend on the wave frequency, the ...

Journal of Offshore Mechanics and Arctic Engineering, 2008

This paper was retracted because it was published in a previous issue, Vol. 129, pp. 306-317 ͑2007͒.

Studies in Applied Mathematics, 2015

In the present study, oblique surface wave scattering by a submerged vertical flexible porous pla... more In the present study, oblique surface wave scattering by a submerged vertical flexible porous plate is investigated in both the cases of water of finite and infinite depths. Using Green's function technique, the boundary value problem is converted into a system of three Fredholm type integral equations. Various integrals associated with the integral equations are evaluated using appropriate Gauss quadrature formulae and the system of integral equations are converted into a system of algebraic equations. Further, using Green's second identity, expressions for the reflection and transmission coefficients are obtained in terms of the velocity potential and its normal derivative. Energy balance relations for wave scattering by flexible porous plates and permeable membrane barriers are derived using Green's identity and used to check the correctness of the computational results. From the general formulation of the submerged plate, wave scattering by partial plates such as (i) surface-piercing and (ii) bottom-standing plates are studied as special cases. Further, oblique wave scattering by bottom-standing and surface-piercing porous membrane barriers are studied in finite water depth as particular cases of the flexible plate problem. Various numerical results are presented to study the effect of structural rigidity, angle of incidence, membrane tension, structural length, porosity and water depth on wave scattering. It is found that wave reflection is more for a surface-piercing flexible porous plate in infinite water depth compared to finite water depth and opposite trend is observed for a submerged flexible porous plate. For a surface-piercing nonpermeable membrane, zeros in transmission coefficient are observed for waves of intermediate water depth

The interaction between current and flexural gravity waves generated due to a floating elastic pl... more The interaction between current and flexural gravity waves generated due to a floating elastic plate is analyzed in two dimensions under the assumptions of linearized theory. For plane flexural gravity waves, explicit expressions for the water particle dynamics and trajectory are derived. The effect of current on the wavelength, phase velocity and group velocity of the flexural gravity waves is analyzed. Variations in wavelength and wave height due to the changes in current speed and direction are analyzed. Effects of structural rigidity and water depth on wavelength are discussed in brief. Simple numerical computations are performed and presented graphically to explain most of the theoretical findings in a lucid manner. r

The effect of compressive force on flexural gravity waves in two-layer fluids is analysed. Wave c... more The effect of compressive force on flexural gravity waves in two-layer fluids is analysed. Wave characteristics for surface and interfacial modes in the cases of deep and shallow water are studied and the effect of compression on these modes is analysed in special cases from the general problem. Generalized expansion formulae and associated orthogonal mode-coupling relations are derived for the velocity potentials to deal with wave structure interaction problems in three dimensions in both the cases of finite and infinite water depths in channels of finite and semi-infinite widths. Several characteristics of the eigenfunctions are derived in specific cases. As an application of the expansion formulae, wave scattering due to partially frozen cracks in floating ice sheet is analysed in a channel of finite width and depth in the presence of compressive force in two-layer fluids.

Using the recently developed expansion formulae for wave structure interaction problems, the scat... more Using the recently developed expansion formulae for wave structure interaction problems, the scattering of surface water waves by a semi-infinite floating membrane due to abrupt change in bottom topography is analyzed. Both the cases of finite and infinite steps are analyzed. In the present paper, the analysis is based on the linearized theory of water waves and small amplitude membrane response. Combining the linearized kinematic and dynamic surface conditions on the water surface with the dynamic pressure condition on the membrane, a third order differential equation is derived to describe the membrane covered free surface condition. General wave energy relation for wave scattering by floating horizontal membrane is derived by the application of law of conservation of energy flux and alternately by the direct application of Green's second identity. In the floating membrane covered region, the wave energy density is a combination of the kinetic and potential energy density due to the surface gravity waves, and the surface energy density which is due to the existence of the floating membrane on the free surface. Gravity wave transformations due to an abrupt change in bottom topography in the presence of a floating membrane in finite water depth are analyzed based on shallow water approximation. Numerical results are computed and analyzed to understand the wave transformation due to the floating membrane when there is an abrupt change in topography in different cases. r

In recent decades, there is growing interest in analyzing the dynamic response of floating elasti... more In recent decades, there is growing interest in analyzing the dynamic response of floating elastic structures with ocean waves which plays a significant role in marine technology and in cold region engineering. These types of problems lead to a special class of boundary value problems associated with Laplace equation having higher order boundary conditions. Recently, developed expansion formulae for such type of wave structure interaction problems based on the direct application of Fourier analysis and Green's integral theorem In the present paper, the expansion formula in quarter plane for a more general type of boundary value problem as in is obtained. The detail derivation of the expansion formula is demonstrated by a different method in a particular case by analyzing the boundary value problem associated with the scattering of surface water waves by a discontinuity in a floating elastic plate.

Zeitschrift für angewandte Mathematik und Physik, 2014

Wave structure interaction problems in a three-layer fluid having an elastic plate covered free s... more Wave structure interaction problems in a three-layer fluid having an elastic plate covered free surface are studied in a three-dimensional fluid domain in both the cases of finite and infinite water depths. Wave characteristics are analyzed from the dispersion relation of the associated wave motion, and approximate results are derived in both the cases of deep water and shallow water waves. Further, the expansion formulae and the associated orthogonal mode-coupling relations are derived for the velocity potentials for the wave structure interaction problems in channels of finite and infinite depths. The utility of the expansion formulae is demonstrated by (1) deriving the source potentials associated with the wave structure interaction problems in a three-layer fluid medium of finite and infinite water depths and (2) analyzing the wave scattering by a partially frozen crack in a floating ice sheet in the three-layer fluid medium in a three-dimensional channel of finite water depth. Various results derived can be used to deal with acoustic wave interaction with flexible structures and other wave structure interaction problems of similar nature arising in different branches of physics and engineering.

Wave Motion, 2008

Expansion formulae for flexural gravity wave problems in two-layer fluids are developed in both t... more Expansion formulae for flexural gravity wave problems in two-layer fluids are developed in both the cases of water of finite and infinite depths. The developed expansion formulae are applied to (i) derive the line source flexural gravity wave potentials in the presence of floating ice sheet of finite thickness and (ii) investigate the scattering of ice-coupled waves by a narrow crack in an infinite floating ice sheet. Both the problems are analyzed in two dimensions in a two-layer fluid having an interface in case of finite and infinite depths separately. Relations based on Green's identity are derived for the reflection and transmission coefficients in surface and interface modes. Effect of the density ratio and the position of interface on the reflection and transmission coefficients and surface and interface elevations in the scattering problem is analyzed.

Ocean Engineering, 2009

In the present study, the effect of shear current on the propagation of flexural gravity waves is... more In the present study, the effect of shear current on the propagation of flexural gravity waves is analyzed under the assumptions of linearized shallow-water theory. Explicit expressions for the reflection and transmission coefficients associated with flexural gravity wave scattering by a step discontinuity in both water depth and current speed are derived. Further, trapping and scattering of flexural gravity waves by a jet-like shear current with a top-hat profile are examined and certain limiting conditions for the waves to exist are derived. The effects of change in water depth, current speed, incident wavelength and the angle of incidence on the group and phase velocities as well as on the reflection and transmission characteristics are analyzed through different numerical results.

Meccanica, 2014

A class of problems associated with forced capillary-gravity wave motion in a channel are analyze... more A class of problems associated with forced capillary-gravity wave motion in a channel are analyzed in the presence of surface and interfacial tensions in a two-layer fluid in both the cases of finite and infinite water depths. The two and three-dimensional Green functions associated with the capillary-gravity wave problems in the presence of surface and interfacial tensions are derived using the fundamental source potentials. Using the two-dimensional Green function along with Green's second identity, the expansion formulae for the velocity potentials associated with the capillary-gravity wavemaker problems in two-dimensions are obtained. The two-dimensional results are generalized to derive the expansion formulae for the velocity potentials associated with the forced capillary-gravity wave motion in the presence of surface and interfacial tensions in three-dimensions. Certain characteristics of the eigen-system associated with the expansion formulae are derived. The velocity potentials associated with the free oscillation of capillary-gravity waves in a closed basin and semiinfinite open channel in the presence of surface and interfacial tensions are obtained. The utility of the forced motion in a channel is demonstrated by analyzing the

Marine Structures, 2005

The wave scattering by an articulated floating elastic plate in water of infinite depth is analyz... more The wave scattering by an articulated floating elastic plate in water of infinite depth is analyzed in the linearized theory of water waves. Using the geometrical symmetry of the articulated plate, the associated boundary value problem in the half-plane is reduced to two boundary value problems in the quarter plane, whose solutions are derived by the direct application of a mixed-type Fourier transform and the corresponding mode-coupling relation. The articulated plate is modeled as the assembling of two semi-infinite thin elastic plates which are attached by connectors. The hydroelastic behavior of the floating elastic plate is investigated by analyzing the stiffness of the connectors on the reflection and transmission characteristics of the flexural gravity waves. The phase and group velocity, reflection and transmission coefficient and the vertical displacement response of the elastic plate are computed and analyzed to understand the effect of articulation on the wave motion below the plate. r

Journal of Fluids and Structures, 2009

Flexural gravity wave scattering by multiple articulated floating elastic plates is investigated ... more Flexural gravity wave scattering by multiple articulated floating elastic plates is investigated in the three cases for water of finite depth, infinite depth and shallow water approximation under the assumptions of two-dimensional linearized theory of water waves. The elastic plates are joined through connectors, which act as articulated joints. In the case when two semi-infinite plates are connected through a single articulation, using the symmetric characteristic of the plate geometry and the expansion formulae for wave-structure interaction problem, the velocity potentials are obtained in closed forms in the case of finite and infinite water depths. On the other hand, in the case of shallow water approximation, the continuity of energy and mass flux are used to obtain a system of equations for the determination of the full velocity potentials for wave scattering by multiple articulations. Further, using the results for single articulation and assuming that the articulated joints are wide apart, the wide-spacing approximation method is used to obtain the reflection coefficient for wave scattering due to multiple articulated floating elastic plates. The effects of the stiffness of the connectors, length of the elastic plates and water depth on the propagation of flexural gravity waves are investigated by analysing the reflection coefficient. r

$Research paper thumbnail of Effect of compression on wave diffraction by a floating elastic plate$

Journal of Fluids and Structures, 2013

In the present paper, the water wave diffraction by a two-dimensional floating elastic plate is a... more In the present paper, the water wave diffraction by a two-dimensional floating elastic plate is analyzed in the presence of compressive force. The solutions in the cases of infinite and finite water depths are derived based on integro-differential equation method in the presence of compressive force under the assumption of small amplitude water wave theory and plate deflection. Further, wave diffraction by the floating elastic plate is analyzed under the assumption of shallow water approximation. The role of compressive force and its limiting values are obtained by using the hydroelastic analysis of the flexural gravity waves. The limiting values of oblique angle of incidence are obtained in different cases and the effect of compressive force on the oblique angle is analyzed. Effect of compressive force and angle of incidence on the hydroelastic behavior of the floating plate are studied by analyzing the reflection coefficients in different cases.

Journal of Fluids and Structures, 2014

In the present study, a combined effect of current and compressive force on time dependent flexur... more In the present study, a combined effect of current and compressive force on time dependent flexural gravity wave motion in both the cases of single and two-layer fluids is analyzed in finite and infinite water depths in two dimensions. The roots of the dispersion relation associated with the plane flexural gravity waves are analyzed via contour plots and by plotting various terms of the dispersion relation separately. The characteristic of plane flexural gravity waves is studied by analyzing the phase and group velocities along with the law of conservation of energy flux to understand the combined effect of current and compressive force on the wave motion. The integral form of the time dependent Green's function in the presence of current is obtained using the Laplace transform method and used in Green's identity to derive the time dependent velocity potential for the flexural gravity wavemaker problem. The time harmonic Green's function and velocity potentials are obtained as a special case from the time dependent problems. Numerical results are computed and analyzed in particular cases using the method of stationary phase to obtain the asymptotic results for Green's function and the deflection of ice sheet. The integral form of Green's function derived here will be suitable to deal with physical problem when the roots of the dispersion relation for the flexural gravity wave problem coalesces which were otherwise not possible in the eigenfunction expansion method used for time harmonic problems.

Journal of Engineering Mathematics, 2011

Generalized expansion formulae for the velocity potentials associated with plane gravity-wave pro... more Generalized expansion formulae for the velocity potentials associated with plane gravity-wave problems in the presence of surface tension and interfacial tension are derived in both the cases of finite and infinite water depths in two-layer fluids. As a part of the expansion formulae, orthogonal mode-coupling relations, associated with the eigenfunctions of the velocity potential, are derived. The dispersion relations are analyzed to determine the characteristics of the two propagating modes in the presence of surface and interfacial tension in both the cases of deep-water and shallow-water waves. The expansion formulae are then generalized to deal with boundary-value problems satisfying higher-order boundary conditions at the free surface and interface. As applications of the expansion formulae, the solutions associated with the source potential, forced oscillation and reflection of capillary-gravity waves in the presence of interfacial tension are derived.