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A theory for wave-power absorption by two independently oscillating bodies

Published online by Cambridge University Press:  19 April 2006

M. A. Srokosz  and
D. V. Evans
M. A. Srokosz
Affiliation:
Department of Mathematics, University of Bristol, England
D. V. Evans
Affiliation:
Department of Mathematics, University of Bristol, England
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Abstract

In a recent paper (Evans 1976) a theory was presented for the behaviour of an oscillating two-dimensional cylinder of any shape which was capable of absorbing energy from a given regular sinusoidal wave. In particular an expression was derived for the efficiency of power absorption of the cylinder when oscillating in a single mode in terms of properties of the solution of the so-called radiation problem in which the cylinder is forced to oscillate in the appropriate mode in the absence of the incident wave train.

In the present paper this theory is extended to two independent cylinders of arbitrary shape each oscillating in a single mode and capable of absorbing energy in that mode. A general expression for the efficiency is derived which depends on properties of the solution to a new radiation problem, in which one cylinder is forced to oscillate in the presence of the other cylinder, which is held fixed in its equilibrium position. In this case, the efficiency also depends on cross-coupling coefficients related to the force on the fixed cylinder due to the motion of the oscillating cylinder.

It is shown that the cylinders can be tuned to absorb all the incident wave energy at a given frequency even for symmetric cylinders, in contrast to the single symmetric cylinder, for which the maximum efficiency has been shown to be 50%.

The general solution to the new radiation problem is derived in terms of the solution to the radiation problem for a single cylinder, by assuming that the cylinders are far enough apart for local wave effects to be negligible.

The special case of two widely spaced rolling vertical plates is considered in detail and curves showing the variation of efficiency with wavelength are given for a variety of plate spacings and points of rotation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 90 , Issue 2 , 29 January 1979 , pp. 337 - 362
Copyright
© 1979 Cambridge University Press

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