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Boundary-layer flow around a submerged circular cylinder induced by free-surface travelling waves

Published online by Cambridge University Press:  26 April 2006

B. Yan
Affiliation:
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK
N. Riley
Affiliation:
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK

Abstract

We consider the fluid flow induced when free-surface travelling waves pass over a submerged circular cylinder. The wave amplitude is assumed to be small, and a suitably defined Reynolds number large, so that perturbation methods may be employed. Particular attention is focused on the steady streaming motion, which induces circulation about the cylinder. The viscous forces acting on the cylinder are calculated and compared with the pressure forces which are solely responsible for the loading on the cylinder in a purely inviscid flow.

Type
Research Article
Copyright
© 1996 Cambridge University Press

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References

Chaplin, J. R. 1984a Mass transport around a horizontal cylinder beneath waves. J. Fluid Mech. 140, 175187.Google Scholar
Chaplin, J. R. 1984b Nonlinear forces on a horizontal cylinder beneath waves. J. Fluid Mech. 147, 449464.Google Scholar
Chaplin, J. R. 1992 Orbital flow around a circular cylinder. Part 1. Steady streaming in non-uniform conditions. J. Fluid Mech. 237, 395411.Google Scholar
Chaplin, J. R. 1993 Orbital flow around a circular cylinder. Part 2. Attached flow at larger amplitudes. J. Fluid Mech. 246, 397418.Google Scholar
Dean, W. R. 1948 On the reflexion of surface waves by a submerged circular cylinder. Proc. Camb. Phil. Soc. 44, 483491.Google Scholar
McIver, M. & McIver, P. 1990 Second-order wave diffraction by a submerged circular cylinder. J. Fluid Mech. 219, 519529.Google Scholar
Riley, N. 1965 Oscillating viscous flows. Mathematika, 12, 161175.Google Scholar
Riley, N. 1967 Oscillatory viscous flows: review and extension. J. Inst. Maths Applics. 3, 419434.Google Scholar
Riley, N. 1971 Stirring of a viscous fluid. Z. Angew Math. Phys. 22, 645653.Google Scholar
Riley, N. 1978 Circular oscillations of a cylinder in a viscous fluid. Z. Angew Math. Phys. 29, 439449.Google Scholar
Riley, N. 1981 High Reynolds number flows with closed streamlines. J. Engng Maths 15, 1527.Google Scholar
Riley, N. & Yan, B. 1996 Inviscid fluid flow around a submerged circular cylinder induced by free-surface travelling waves. J. Engng Maths (to be published).Google Scholar
Stansby, P. K. & Smith, P. A. 1991 Viscous forces on a circular cylinder in orbital flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 229, 159171.Google Scholar
Stuart, J. T. 1966 Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24, 673687.Google Scholar
Ursell, F. 1950 Surface waves on deep water in the presence of a submerged circular cylinder. I. Proc. Camb. Phil. Soc. 46, 141152.Google Scholar
Vada, T. A. 1987 A numerical solution of the second-order wave-diffraction problem for a submerged cylinder of arbitrary shape. J. Fluid Mech. 174, 2337.Google Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. In Encyclopedia of Physics, Volume IX, Fluid Dynamics III (ed. S. Flügge), pp. 446778. Springer.
Wu, G. X. 1991 On the second order wave reflection and transmission by a horizontal cylinder. Appl. Ocean Res. 13, 5862.Google Scholar
Zapryanov, Z., Kozhoukharova, Zh. & Iordanova, A. 1988 On the hydrodynamic interaction of two circular cylinders oscillating in a viscous fluid. Z. Angew Math. Phys. 39, 204219.Google Scholar