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Tidal diffraction by a small island or cape, and tidal power from a coastal barrier

Published online by Cambridge University Press:  11 June 2020

Chiang C. Mei Open the ORCID record for Chiang C. Mei [Opens in a new window]
Chiang C. Mei*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA02139-4307, USA
*
†Email address for correspondence: [email protected]
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Abstract

The tidal waves scattered by a small island and a small cape of elliptical shape are derived by the method of matched asymptotics. The results complement the irrotational flow approximation of the near field by Proudman (Proc. Lond. Math. Soc., vol. 14, 1915, pp. 89–102). The potential for harnessing tidal power is assessed for the limiting case of a coast-connected thin dam.

JFM classification

Geophysical and Geological Flows: Waves in rotating fluids Geophysical and Geological Flows: Coastal engineering
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 897 , 25 August 2020 , A13
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Abel-Hafz, A. M., Essawy, A. H. & Moubark, M. A. M. 1997 The diffraction of Kelvin waves due to an island. J. Comput. Appl. Maths 84 (1997), 147–160.CrossRefGoogle Scholar
Al-Hawaj, A. G., Essawy, A. H. & Faltas, M. S. 1991 The diffraction of Kelvin wave due to a narrow headland normal to an infinite coastline. Acta Mechanica 86, 53–63.CrossRefGoogle Scholar
Baker, A. C. 2000 Tidal Power. IET Energy Series.Google Scholar
Buchwald, V. T. 1971 The diffraction of tides by a narrow channel. J. Fluid Mech. 46, 501–511.CrossRefGoogle Scholar
Buchwald, V. T. & Miles, J. W. 1974 Kelvin wave diffraction by a gap. J. Austral. Math. Soc. 17, 29–34.CrossRefGoogle Scholar
Crighton, D. G. & Leppington, F. G. 1973 Singular perturbation methods in acoustics: diffraction by a plate of finite thickness. Proc. R. Soc. Lond. A 335, 313–339.Google Scholar
Crease, J. 1956 Long waves on a rotating earth in the presence of a semi-infinite barrier. J. Fluid Mech. 1, 86–96.CrossRefGoogle Scholar
Dai, P., Zhang, J.-S & Zheng, J.-H 2017 Predictions for dynamic tidal power and asociated local hydrodynamic impact in the Taiwan strait, China. J. Coast. Res. 33 (1), 149–157.CrossRefGoogle Scholar
Dai, P., Zhang, J.-S, Zheng, J.-H, Hulsbergen, K., van Banning, G., Adema, J. & Tang, Z.-X. 2018 Numerical studies of hydrodynamic mechanisms of dynamic tidal power. Water Sci. Engng 11 (3), 220–228.CrossRefGoogle Scholar
Essawy, A. H. 1984 The diffraction of a Kelvin wave due to a narrow island normal to an infinite coastline. Arch. Mech. 36 (1), 21–31.Google Scholar
Essawy, A. H. 1995 Diffraction of a Kelvin wave by a circular island using a Green’s function technique. Bull. Cal. Math. Soc. 87, 501–510.Google Scholar
Gradshteyn, I. S. & Rizhik, I. M. 1980 Table of Integrals, Series and Products. Academic.Google Scholar
Guo, S. & McIver, P. 2011 Propagation of elastic waves through a lattice of cylindrical cavities. Proc. R. Soc. Lond. 467 (2134), 2962–2982.CrossRefGoogle Scholar
Hildebrand, F. S. 1976 Advanced Calculus for Applications. Prentice-Hall.Google Scholar
Howe, M. S. & Mysak, L. A. 1973 Scattering of Poincare waves by an irregular coastline. J. Fluid Mech. 57, 111–128.CrossRefGoogle Scholar
Hulsbergen, K., Steijn, R., Hassan, R., Klopman, G. & Hurdle, D. 2005 Dynamic Tidal Power (DTP). In 6th European Wave and Tidal Energy Conf. Glasgow UK, pp. 217–222.Google Scholar
Hulsbergen, K., de Boer, Steijn, R. & van Banning, G. 2008a Dynamic tidal power for Korea. In 1st Asian Wave and Tidal Conference Series, pp. 1–8.Google Scholar
Hulsbergen, K., Steijn, R., van Banning, G., Klopman, G. & Frölich, A. 2008b Dynamic Tidal Power – A new approach to exploit tides. In 2nd Int. Conf. on Ocean Energy, Brest, France, pp. 1–10.Google Scholar
Kleinman, R. & Vainberg, B. 1994 Full low-frequency asymptotic expansion for secondorder elliptic equations in two dimensions. Math. Meth. Appl. Sci. 17 (12), 989–1004.CrossRefGoogle Scholar
Klopman, G.2003, Hydrodynamic simulation tool of Active Tidal Power Plant. Report D18.00-01. Albatros Flow Research, Inc.Google Scholar
Krutitskii, P. A. 2001 The oblique derivative problem for the Helmholtz equation and scattering tidal waves. Proc. R. Soc. Lond. A 457, 1735–1755.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics, p. 530. Dover.Google Scholar
LeBlond, P. H. & Mysak, L. A. 1987 Waves in the Ocean. Elsevier.Google Scholar
Liu, Q. & Zhang, W.-L. 2014 Hydrodynamic study of phase-shift tidal power system with Y-shaped dams. J. Hydraul Res. 52 (3), 356–365.Google Scholar
Martin, P. A. 2006 Multiple Scattering. Cambridge University Press.CrossRefGoogle Scholar
Martin, P. A. 2001 On the diffraction of Poincaré waves. Math. Meth. Appl. Sci. 24, 13–925.Google Scholar
Martin, P. A. & Dalrymple, R. A. 1988 Scattering of long waves by cylindrical obstacles and gratings using matched asymptotic expansions. J. Fluid Mech. 188, 465–490.CrossRefGoogle Scholar
Mei, C. C. 2012 Note on tidal diffraction by a coastal barrier. Appl. Ocean Res. 36, 22–25.CrossRefGoogle Scholar
Milne-Thomson, L. M. 1955 Theoretical Hydrodynamics. Macmillan.Google Scholar
Pinsent, H. G. 1971 The effect of a depth discontinuity on Kelvin wave diffraction. J. Fluid Mech. 45, 747–758.CrossRefGoogle Scholar
Pinsent, H. G. 1972 Kelvin wave attenuation along nearly straight boundaries. J. Fluid Mech. 53 (2), 273–286.CrossRefGoogle Scholar
Proudman, J. 1915 Diffraction of tidal waves on flat rotating sheet of water. Proc. Lond. Math. Soc. 14, 89–102.CrossRefGoogle Scholar
Proudman, J. 1953 Dynamical Oceanography. Methuen.Google Scholar
Rhines, P. B. 1969a Slow oscillations in an ocean of varying depth. Part 1. Abrupt topography. J. Fluid Mech. 37, 161–189.CrossRefGoogle Scholar
Rhines, P. B. 1969b Slow oscillations in an ocean of varying depth. Part 2. Islands and seamounts. J. Fluid Mech. 37, 191–205.CrossRefGoogle Scholar
Stamnes, J. J. & Spjelkavik, B. 1995 New method for computing eigenfunctions (Mathieu functions) for scattering by elliptical cylinders. Pure Appl. Opt. J. Eur. Opt. Soc. Part A 4, 251–262.CrossRefGoogle Scholar
Strutt, J. W. (Lord Rayleigh) 1897 On the incidence of aerial and electric waves upon small obstacles in the form of ellipsoids or elliptic cylinders, and on the passage of electric waves through a circular aperture in a conducting screen. Phil. Mag. XLIV, 2–52.Google Scholar
Varadan, V. K. & Varadan, V. V.(Eds) 1968 Low and High Frequency Asymptotics – Acoustic, Electromagnetic and Elastic Wave Scattering. North Holland.Google Scholar
Zhou, J.-T., Falconer, R. A. & Lin, B.-L. 2014 Refinement to the EFDC model for predicting the hydro-environmental impacts of barrage across the Severn Estuary. Renew. Energy 62, 491–505.CrossRefGoogle Scholar