The effect of submergence on the scattering by the interface between two semi-infinite sheets

Williams, Timothy; Porter, Robert

doi:10.1016/j.jfluidstructs.2009.02.001

Cited by 31 publications

(20 citation statements)

References 16 publications

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“…This is analogous to the perfect transmission produced by a crack. However, it is known that when an Archimedean draught is included this resonance is eliminated (Williams & Porter 2009), and is actually displaced into the oblique incidence regime.…”

Section: (B) Floesmentioning

confidence: 99%

On the calculation of an attenuation coefficient for transects of ice-covered ocean

Bennetts

Squire

2011

Proc. R. Soc. A.

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Exponential attenuation of ocean surface waves in ice-covered regions of the polar seas is modelled in a two-dimensional, linear setting, assuming that the sea ice behaves as a thinelastic plate. Attenuation is produced by natural features in the ice cover, with three types considered: floes, cracks and pressure ridges. An inelastic damping parameterization is also incorporated. Efficient methods for obtaining an attenuation coefficient for each class of feature, involving an investigation of wave interaction theory and averaging methods, are sought. It is found that (i) the attenuation produced by long floes can be obtained from the scattering properties of a single ice edge; and (ii) wave interaction theory in ice-covered regions requires evanescent and damped-propagating motions to be included when scattering sources are relatively nearby. Implications for the integration of this model into an oceanic general circulation model are also discussed.

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Section: (B) Floesmentioning

confidence: 99%

On the calculation of an attenuation coefficient for transects of ice-covered ocean

Bennetts

Squire

2011

Proc. R. Soc. A.

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“…Although we do not include the performance of the EM method for the free-edge conditions here, we found that its convergence was similar to the case where the clamped-edge conditions were applied-reflecting the fact the main obstacle that it needs to overcome is in capturing the singularity in the flow near the plate edge. Note that the slow convergence of the EM could be improved by adapting the method of Williams and Porter [29]. Although we have not yet implemented this method ourselves, this would be extremely useful as it could also be generalized to solve a similar problem, that of a submerged circular flexible disc [20].…”

Section: Resultsmentioning

confidence: 99%

“…Although we have not yet implemented this method ourselves, this would be extremely useful as it could also be generalized to solve a similar problem, that of a submerged circular flexible disc [20]. The improvement in convergence expected would be significant as Williams and Porter [29] only needed to solve a very small linear system (5-20 unknowns) to obtain well-converged results.…”

Section: Resultsmentioning

confidence: 99%

“…It is more difficult to prove what the value of υ should be when the thin-plate condition is applied, but by using an analytical solution method in this article, we are able to determine it directly (indeed we find that υ = 1 2 in this case also). Note also that this edge condition does not appear in the standard EM method, but it can be included using the method outlined by Williams and Porter [29].…”

Section: Problem Formulationmentioning

confidence: 99%

“…It is not known how to apply the RC and WH methods as generally as the EM method though, for example, at present, we cannot solve problems with circular geometries [20], which can be done with EM. However, WH and RC can be used to tackle a single plate of finite length, whether directly [18,19,28] or by using transfer matrices to extend the semi-infinite results [29].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Wiener–Hopf and residue calculus solutions for a submerged semi-infinite elastic plate

Williams¹,

Meylan

2011

J Eng Math

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We present a solution for the interaction of normally incident linear waves with a submerged elastic plate of semi-infinite extent, where the water has finite depth. While the problem has been solved previously by the eigenfunction-matching method, the present study shows that this problem is also amenable to the more analytical, and extremely efficient, Wiener-Hopf (WH) and residue calculus (RC) methods. We also show that the WH and RC solutions are actually equivalent for problems of this type, a result which applies to many other problems in linear wave theory. (e.g., the much-studied floating elastic plate scattering problem, or acoustic wave propagation in a duct where one wall has an abrupt change in properties.) We present numerical results and a detailed convergence study, and discuss as well the scattering by a submerged rigid dock, particularly the radiation condition beneath the dock.

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Integral equation technique for water wave interaction by an array of vertical flexible porous wave barriers

Koley

Sahoo

2020

Z Angew Math Mech

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Scattering of obliquely incident surface gravity waves by an array of partial flexible vertical porous wave barriers of varied configurations is studied in finite water depth and deep water cases. For the mathematical modeling purpose, linearized water wave theory is considered. Firstly, the problem associated with double vertical barriers is handled for a solution. To solve the problem, the associated BVP (boundary value problem) is transformed into a system of Fredholm integral equations of the second kind. By using suitable quadrature formulae, these integral equations are converted to a system of linear algebraic equations. These are solved to compute various important physical quantities associated with wave scattering. The energy identities for both finite water depth and deep water cases are derived. These derived energy identities are used to check the computational accuracy and to quantify the loss of wave energy by the barrier system. Subsequently, the study is extended to deal with wave scattering by multiple non‐identical unequally spaced barriers using wide‐spacing approximation and results for equally spaced identical barriers are obtained as a special case. The methodology is further generalized to deal with Bloch problem to incorporate a periodic array of infinite barriers. Occurrences of Bragg resonance in case of multiple barriers are analyzed. From the results associated with the linearized water wave theory, the second‐order mean wave forces are computed and compared with the first‐order wave forces. The phenomena of cloaking for wave scattering by multiple impervious barriers are discussed for a wide variety of wave and structural parameters. The methodology used in this present study can easily be generalized to solve similar problems that arise in mathematical physics.

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The effect of submergence on the scattering by the interface between two semi-infinite sheets

Cited by 31 publications

References 16 publications

On the calculation of an attenuation coefficient for transects of ice-covered ocean

On the calculation of an attenuation coefficient for transects of ice-covered ocean

The Wiener–Hopf and residue calculus solutions for a submerged semi-infinite elastic plate

Integral equation technique for water wave interaction by an array of vertical flexible porous wave barriers

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