Scattering by periodic array of rectangular blocks

Fernyhough, M.; Evans, D. V.

doi:10.1017/s0022112095004629

Cited by 43 publications

(13 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Mathematically, if we directly match eigenfunction expansions at these places, there are numerical difficulties [15,16]. To handle these singularities in the velocity field, Porter & Evans [15], Fernyhough & Evans [17], Chang et al [18] and Deng et al [12] introduced auxiliary functions to represent the unknown radial velocities on the common interfaces, which involve singular behaviours at incontinuous tips or corners.…”

Section: Introductionmentioning

confidence: 99%

Wave power extraction from a bottom-mounted oscillating water column converter with a V-shaped channel

2014

View full text Add to dashboard Cite

An analytical theory is developed for an oscillating water column (OWC) with a V-shaped channel to improve the pneumatic efficiency of wave energy extraction. An eigenfunction expansion method is used in a cylindrical coordinate system to investigate wave interaction with the OWC converter system. Auxiliary functions are introduced to capture the singular behaviours in the velocity field near the salient corners and cusped edges. Effects of the OWC dimensions, the opening angle and length of the V-shaped channel, as well as the incident wave direction, on the pneumatic efficiency of wave energy extraction are examined. Compared with a system without the V-shaped channel, our results show that the V-shaped channel can significantly increase the conversion efficiency and widen the range of wave frequency over which the OWC system can operate at a high efficiency. For typical coastal water depths, the OWC converter system can perform efficiently when the diameter of the OWC chamber is in the range of 1 5 -1 2 times the water depth, the opening angle of the V-shaped channel is in the range of [π/2, 3π/4] and the length of the V-shaped channel is in the range of 1-1.5 times the water depth.

show abstract

Section: Introductionmentioning

confidence: 99%

Wave power extraction from a bottom-mounted oscillating water column converter with a V-shaped channel

2014

View full text Add to dashboard Cite

show abstract

“…The problem of Twersky [9], who used Schlömilch series to sum slowly convergent series involving Hankel functions, was re-considered by Linton and Evans [10] who used a so-called multipole method. For periodic arrays of rectangular cylinders extending uniformly through the depth, Fernyhough and Evans [11] used domain decomposition and mode matching to derive an integral-equation formulation to the problem. In order to consider more general cylinder profiles, boundary-integral methods are inevitable and require the use of a periodic Green function.…”

Section: Introductionmentioning

confidence: 99%

The linear-wave response of a periodic array of floating elastic plates

Meylan

Porter

2006

J Eng Math

View full text Add to dashboard Cite

The problem of an infinite periodic array of identical floating elastic plates subject to forcing from plane incident waves is considered. This study is motivated by the problem of trying to model wave propagation in the marginal ice zone, a region of ocean consisting of an arbitrary packing of floating ice sheets. It is shown that the problem considered can be formulated exactly in terms of the solution to an integral equation in a manner similar to that used for the problem of wave scattering by a single elastic floating plate, the key difference here being the use of a modified periodic Green function. The convergence of this Green function in its original form is poor, but can be accelerated by a transformation. It is shown that the results from the method satisfy energy conservation and that in the particular case of a fixed rigid rectangular plate which spans the periodicity uniformly the solution reduces to that for a two-dimensional rigid dock. Solutions for a range of elastic-plate geometries are also presented.

show abstract

“…For example, Linton & Evans (1993) demonstrate total transmission of oblique wave energy past an infinite periodic row of rigid circular cylinders. When the circular cylinders are replaced by rectangular cylinders Fernyhough & Evans (1995) give extensive results illustrating total transmission for a variety of incident wave angles; also see Yang et al (2011) who consider a similar problem in an electromagnetic context. Porter & Evans (1996) considered oblique wave transmission through infinitesimally-thin screens incorporating a periodic arrangement of gaps, a problem with a long history: see, for example, Jones (1986) in the electromagnetic context.…”

Section: Introductionmentioning

confidence: 99%

Total transmission of waves through narrow gaps in channels

Evans¹,

Porter

2017

The Quarterly Journal of Mechanics and Applied Mathematics

Self Cite

View full text Add to dashboard Cite

The problem of the transmission of plane waves along a uniform parallel-walled waveguide or channel through a periodically-spaced array of thin screens with gaps placed across the channel is investigated. Of particular interest is the existence of frequencies at which energy it totally transmitted -shown to occur when there are two or more screens -and how they depend upon the size of the gaps in the screen. Attention focuses on small gaps where the phenomenon of total transmission persists and where an approximate analysis of a system of full coupled integrals equations is reduced to simple linear difference equations which can be solved in closed form. Results show comparisons between exact computations, the small-gap computations and corresponding wide-spacing approximations. A discussion of total reflection is also included when the gaps are no longer assumed to be small.

show abstract

Scattering by periodic array of rectangular blocks

Cited by 43 publications

References 7 publications

Wave power extraction from a bottom-mounted oscillating water column converter with a V-shaped channel

Wave power extraction from a bottom-mounted oscillating water column converter with a V-shaped channel

The linear-wave response of a periodic array of floating elastic plates

Total transmission of waves through narrow gaps in channels

Contact Info

Product

Resources

About