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Nonlinear resonance in Anaconda

Published online by Cambridge University Press:  10 June 2014

Chiang C. Mei
Chiang C. Mei*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, MA 02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

A nonlinear theory is developed for a recent wave energy converter design inspired by the mechanics of animal arteries. The device is a long and hollow rubber tube immersed beneath the sea surface. Excited by passing water waves outside, pressure waves are resonated inside the tube and advance toward the stern to spin a turbine for power production. To account for significant magnification, the classical linear theory of blood vessels is modified. Diffraction is neglected but nonlinearity and wall friction are included. The spatial evolution of harmonic amplitudes is shown to be governed by a dynamical system similar to that in nonlinear optics. The maximum available power flux is predicted as a function of the tube length and other structural parameters. It is hoped that the theory may assist further development of the novel device.

JFM classification

Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 750 , 10 July 2014 , pp. 507 - 517
Copyright
© 2014 Cambridge University Press 

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References

Anliker, M., Rockwell, R. L. & Ogden, E. 1971 Nonlinear analysis of flow pulses and shock waves in arteries. Z. Angew. Math. Phys. 22, 217–246.CrossRefGoogle Scholar
Armstrong, J. A., Bloembergen, N., Ducuing, J. & Pershan, P. S. 1962 Interaction between light waves in a nonlinear dielectric. Phys. Rev. 127, 1918–1939.CrossRefGoogle Scholar
Bryant, P. J. 1983 Periodic waves in shallow water. J. Fluid Mech. 59, 624–644.Google Scholar
Chaplin, J. R., Heller, V., Farley, F. J. M. & Hearn, G. E. 2012 Laboratory testing the Anaconda. Phil. Trans. R. Soc. Lond. 370, 403–424.Google Scholar
Collins, J. I. 1963 Inception of turbulence at the bed under periodic gravity waves. J. Geophys. Res. 18, 6007–6014.Google Scholar
Farley, F. J. M., Rainey, R. C. T. & Chaplin, J. R. 2012 Rubber tubes in the sea. Phil. Trans. R. Soc. Lond. 370, 381–402.Google Scholar
Fung, Y. C. 1996 Biomechanics: Circulation. Springer.Google Scholar
Grant, W. H. & Madsen, O. S. 1979 Combined wave and current interaction with rough bottom. J. Geophys. Res. 84, 1797–1808.Google Scholar
Grataloup, G. & Mei, C. C. 2003 Localization of harmonics generated in nonlinear shallow water waves. Phys. Rev. E 68, 026314.CrossRefGoogle ScholarPubMed
Haren, P. & Mei, C. C. 1981 Head-sea diffraction by a slender raft with application to wave-power absorption. J. Fluid Mech. 104, 505–526.CrossRefGoogle Scholar
Hino, M., Sawamoto, M. & Takasu, S. 1976 Experiments on transition to turbulence in an oscillatory pipe flow. J. Fluid Mech. 75, 193–207.CrossRefGoogle Scholar
Jonsson, I. G.1966 Wave boundary layers and friction factors. In Proceedings of 10th Conference Coastal Eng. ASCE, pp. 127–148.Google Scholar
Kajiura, K. 1968 A model of the bottom boundary layer in water waves. Bull. Earthq. Res. Inst., Univ. Tokyo 46, 75–123.Google Scholar
Li, H.1954 Stability of an oscillatory laminar flow along a wall. US Army, Beach Erosion Board Tech. Memo. 47.Google Scholar
McDonald, D. A. 1974 Blood Flow in Arteries. Edward Arnold.Google Scholar
Mei, C. C., Stiassnie, M. & Yue, D. K.-P. 2005 Theory and Applications for Ocean Surface Waves. vol. II. World Scientific.Google Scholar
Mei, C. .C. & Ünlüata, Ü. 1973 Harmonic generation in shallow water waves. In Waves on Beaches (ed. Meyer, R. E.), pp. 181–202. Academic Press.Google Scholar
Newman, J. N. 1979 Absorption of wave energy by elongated bodies. Appl. Ocean Res. 1, 189–196.Google Scholar
Olsen, J. H. & Shapiro, A. H. 1967 Large-amplitude unsteady flow in liquid-filled elastic tubes. J. Fluid Mech. 29, 513–538.Google Scholar
Pedley, T. M. 1980 The Fluid Mechanics of Large Blood Vessels. Cambridge University Press.Google Scholar
Rogers, S. R. & Mei, C. C. 1987 Nonlinear resonant excitation of a long and narrow bay. J. Fluid Mech. 88, 463–479.Google Scholar
Yomosa, S. 1987 Solitary waves in large blood vessels. J. Phys. Soc. Japan 56 (2), 506–520.Google Scholar