An explicit solution is provided for the scattering of flexural and membrane-coupled gravity waves in deep water against a complete vertical porous barrier by employing certain mode-coupling relations. The floating structure is considered to be attached with the vertical porous barrier in three different ways, giving rise to edge conditions: (i) free edge, (ii) simply supported edge, (iii) clamped or built-in edge in the case of a floating ice-sheet and to fixed or clamped edge condition in the case of a floating membrane. The effect of the porous barrier on these structure-coupled gravity waves is discussed numerically by plotting reflection coefficient against a wave parameter. Also, important physical quantities such as strain in the ice-sheet, shear force in the ice-sheet and ice-sheet deflections are computed and plotted against relevant parameters. The effect of compressive force on flexural gravity wave scattering is also included in the numerical study. © IMechE 2013.

Srinivasa Rao Manam

Department of Mathematics

Compressive forces

Explicit solutions

FLEXURAL-GRAVITY WAVES

FLOATING STRUCTURES

Mixed boundary-value problem

MODE COUPLING

Physical quantities

POROUS EFFECT PARAMETER

Gravity Waves

Reflection

Boundary value problems

Glaciers

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Structure-coupled gravity waves past a vertical porous barrier

Proceedings of the Institution of Mechanical Engineers Part M: Journal of Engineering for the Maritime Environment

Two-dimensional linear flexural gravity wave scattering by a nearly vertical porous wall is analyzed through a simplified perturbational analysis. A continuous semi-infinite ice sheet of uniform thickness is assumed to be floating over water of infinite depth. The ice sheet, with inclusion or exclusion of compressive stress, has either a free edge or a clamped edge at the porous wall. The first-order correction to the reflected flexural gravity wave amplitude is obtained by two different methods. The first method involves an application of Green’s theorem, and the second method involves a first kind integral equation. The integral equation method proves to be robust as it provides a complete solution in all cases of the problem, whereas the first method fails to produce the same when the ice sheet with a free edge is under compressive stress. The strain in the ice sheet and shear force along the ice sheet are computed and explained graphically for suitable parameters and a particular wall shape function. © 2014, Springer Science+Business Media Dordrecht.

Journal of Engineering Mathematics

Flexural gravity wave scattering by a nearly vertical porous wall

An explicit solution is provided for the scattering of flexural gravity waves by a rigid vertical barrier submerged in an infinite depth of water. By applying recently developed mode-coupling relation for eigenfunctions, the mixed boundary value problem has been converted to solve dual integral equations with kernel consisting of trigonometric functions. And then complete analytical solutions are derived with an aid of singular integral equations whose solutions are bounded at the end points. The important hydrodynamical scattering quantities such as reflection and transmission coefficients associated with the flexural gravity wave scattering have been obtained analytically in terms of modified Bessel functions and Struve functions. It is observed that these quantities are sensitive to both combined as well as individual effect of plate thickness and barrier depth of submergence. Numerical results are computed and explained graphically for different parameters such as time period and non-dimensional wave length. Further, the effect of compressive force and plate thickness on the flexural gravity waves against a submerged vertical barrier is studied. © 2011 Elsevier Ltd. All rights reserved.

International Journal of Engineering Science

Effect of a submerged vertical barrier on flexural gravity waves

Scattering of membrane coupled gravity waves in deep water by partial vertical barriers is investigated by the recently developed expansion formulae for wave structure interaction problems. The horizontal thin membrane is considered to be under uniform tension and is covering the free surface. The analysis is based on the linearized theory of water waves, and by combining the kinematic and dynamic conditions at the membrane covered surface, one may derive a not so well-posed mixed boundary value problem for Laplaces equation with third-order boundary condition. The flexible membrane is attached by a spring to the surface piercing barrier, giving suitable edge conditions for the unique solution. The boundary value problem has been converted into dual integral equations with kernels composed of trigonometric functions, which are then solved analytically. The important physical quantities such as reflection and transmission coefficients for both cases of submerged and surface piercing barriers are obtained analytically in terms of modified Bessel functions. It is found that complete reflection or transmission is possible at certain resonant frequencies for the incident membrane coupled waves. Numerical results are plotted and discussed for different values of the nondimensional membrane tension parameter. © 2010 Australian Mathematical Society.

Journal	Proceedings of the Institution of Mechanical Engineers Part M: Journal of Engineering for the Maritime Environment
ISSN	14750902
Open Access	No