Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-19T15:20:10.162Z Has data issue: false hasContentIssue false

Orbital flow around a circular cylinder. Part 1. Steady streaming in non-uniform conditions

Published online by Cambridge University Press:  26 April 2006

John R. Chaplin
Affiliation:
Ocean Engineering Research Centre, Department of Civil Engineering, City University, London EC1V 0HB, UK

Abstract

This work is concerned with the source of an important component of nonlinear loading on a horizontal cylinder beneath waves that is not present in conventional diffraction calculations. Earlier measurements (Chaplin 1984b) have suggested that circulation induced by steady streaming around the cylinder may be responsible for loading which in some cases reduces the perceived inertia force by 50%. The present work is aimed at studying the steady streaming around a cylinder in general non-uniform orbital flow, and determining whether in the particular case of wave-induced flow it could be related quantitatively to the loading.

The steady outer flow has been obtained numerically for cases where the steady streaming does not have a reversal, and for cases where a weak reversal is compatible with a uniform outer circulation. It is found that the outer circulation is closely related to the mean streaming velocity around the cylinder at the outer edge of the shear-wave layer. Results for conditions corresponding to previous measurements of force on a horizontal cylinder beneath waves suggest that separation, turbulence, transient effects and organized three-dimensional instabilities should also be considered.

Type
Research Article
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chaplin, J. R. 1981 On the irrotational flow around a horizontal cylinder in waves. Trans. ASME E: J. Appl. Mech. 48, 689694Google Scholar
Chaplin, J. R. 1984a Mass transport around a horizontal cylinder beneath waves. J. Fluid Mech. 140, 140175.Google Scholar
Chaplin, J. R. 1984b Forces on a horizontal cylinder beneath waves. J. Fluid Meeh. 147, 147449.Google Scholar
Chaplin, J. R. 1988 Non-linear forces on horizontal cylinders in the inertia regime in waves at high Reynolds numbers. Proc. Intl BOSS Conf, Trondheim, pp. 505518.Google Scholar
Chaplin, J. R. 1992 Orbital flow around a circular cylinder: Part 2. Attached flow at larger amplitudes. J. Fluid Mech. (submitted).Google Scholar
Faraday, M. 1831 On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating surfaces. Phil. Trans. R. Soc. Lond. 121, 299340.Google Scholar
Honji, H. 1981 Streaked flow around an oscillating circular cylinder. J. Fluid Mech. 107, 509520.Google Scholar
Kim, S. K. & Troesch, A. W. 1989 Streaming flows generated by high frequency small-amplitude oscillations of arbitrarily shaped cylinders. Phys. Fluids A 1, 975985.Google Scholar
Kubo, S. & Kitano, Y. 1980 Secondary flow induced by a circular cylinder oscillating in two directions. J. Phys. Soc. Japan 49, 20262037.Google Scholar
Kusukawa, K., Shimizu, Y. & Shinoda, A. 1980 The secondary flow about a circular cylinder oscillating rotationally around an eccentric axis. J. Phys. Soc. Japan 49, 24002406.Google Scholar
Longuet-Higgins, M. S. 1970 Steady currents induced by oscillations round islands. J. Fluid Mech. 42, 701720.Google Scholar
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics, 5th edn. Macmillan.
Ogilvie, T. F. 1963 First- and second-order forces on a cylinder submerged under a free surface. J. Fluid Mech. 16, 451472.Google Scholar
Rayleigh, Lord 1883 On the circulation of air in Kundt's tubes and on some allied acoustical phenomena. Phil. Trans. R. Soc. Lond., 175, 121.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
Sarpkaya, T. 1986 Force on a circular cylinder in viscous oscillatory flow at low Keulegan-Carpenter numbers. J. Fluid Mech. 165, 6171.Google Scholar
Taneda, S. 1980 Visualisation of steady flows induced by a circular cylinder performing a rotary oscillation about an eccentric axis. J. Phys. Soc. Japan 49, 20382041.Google Scholar
Wang, J. C. T. & Shen, S. F. 1978 Unsteady boundary layers with flow reversal and the associated heat-transfer problem. AIAA J. 16, 10251029.Google Scholar