Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

Chakrabarti, A.; Mohapatra, Smrutiranjan

doi:10.1007/s11804-013-1204-z

Cited by 15 publications

(5 citation statements)

References 10 publications

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“…Out of many important results in the study of scattering of water waves, the special relation known as "energy balance relation or energy identity" plays a very important role for checking the method of solution of mixed boundary value problem arises in water wave theory. The energy identity [6] relates the reflection as well as transmission coefficients associated with the scattering problem, which supports the theoretical validation of the present problem in the absence of experimental evidences. In a two-layer fluid system, the presence of surface tension leads to two distinct energy identities corresponding to incident waves of both wave numbers.…”

Section: Energy Identitiessupporting

confidence: 81%

Water-Waves Scattering by Permeable Bottom in Two-Layer Fluid in the Presence of Surface Tension

Panda

Martha

2017

Mathematical Modelling and Analysis

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In the present paper, reflection and transmission phenomena of water waves due to undulating permeable bottom in a two-layer fluid system are investigated using two-dimensional linearized theory. The effect of surface tension on the free surface is included in this work. In two-layer fluid system, there exist waves with two different wave numbers (modes). When a wave of a particular wave number encounters the undulating bottom, reflection and transmission phenomena occur in both the layers. The reflection and transmission coefficients in both layers due to incident waves of both modes are analyzed with the aid of perturbation analysis along with Fourier transform technique. It is found that these coefficients are obtained in terms of integrals which depend on the shape function of the undulating bottom. Two different kinds of undulating bottoms are considered to determine these coefficients. For a particular undulating bottom, namely sinusoidal bottom undulation the effect of various physical parameters such as number of ripples, surface tension and porous effect parameters are demonstrated graphically. The study further elaborates the energy balance relations associated with the reflection and transmission coefficients to ascertain the correctness of all the computed results.

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Section: Energy Identitiessupporting

confidence: 81%

Water-Waves Scattering by Permeable Bottom in Two-Layer Fluid in the Presence of Surface Tension

Panda

Martha

2017

Mathematical Modelling and Analysis

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“…In the case of identical plates, energy identity (B 5) has the form (A 6a−c). Energy-balance relation for non-identical plates was given by Chakrabarti & Mohapatra (2013) in the form…”

Section: Appendix a Surface Wave Diffraction On A Floating Elastic Pmentioning

confidence: 99%

Radiation of waves by a cylinder submerged in water with ice floe or polynya

Sturova

2015

J. Fluid Mech.

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The problems of radiation (sway, heave and roll) of surface and flexural-gravity waves by a submerged cylinder are investigated for two configurations, concerning; (i) a freely floating finite elastic plate modelling an ice floe, and (ii) two semi-infinite elastic plates separated by a region of open water (polynya). The fluid of finite depth is assumed to be inviscid, incompressible and homogeneous. The linear two-dimensional problems are formulated within the framework of potential-flow theory. The method of mass sources distributed along the body contour is applied. The corresponding Green's function is obtained by using matched eigenfunction expansions. The radiation load (added mass and damping coefficients) and the amplitudes of vertical displacements of the free surface and elastic plates are calculated. Reciprocity relations which demonstrate both symmetry of the radiation load coefficients and the relation of damping coefficients with the far-field form of the radiation potentials are found. It is shown that wave motion essentially depends on the position of the submerged body relative to the elastic plate edges. The results of solving the radiation problem are compared with the solution of the diffraction problem. It is noted that resonant frequencies in the radiation problem correlate with those frequencies at which the reflection coefficient in the diffraction problem has a local minimum.

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“…In the study of problems involving scattering of water waves, the special relation known as energy identity or energy balance relation (Chakrabarti and Martha, 2009;Chakrabarti and Mohapatra, 2013) gives a mathematical expression involving the physical quantities, namely, the reflection and transmission coefficients associated with a scattering problem under consideration. This relation helps in ensuring the correctness of the method of solution.…”

Section: Energy Balance Relationmentioning

confidence: 99%

Diffraction of surface water waves by an undulating bed topography in the presence of vertical barrier

Choudhary

Martha

2016

Ocean Engineering

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Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

Cited by 15 publications

References 10 publications

Water-Waves Scattering by Permeable Bottom in Two-Layer Fluid in the Presence of Surface Tension

Water-Waves Scattering by Permeable Bottom in Two-Layer Fluid in the Presence of Surface Tension

Radiation of waves by a cylinder submerged in water with ice floe or polynya

Diffraction of surface water waves by an undulating bed topography in the presence of vertical barrier

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