_ Vol. 26 (2) (2000) pp. 69-94 _
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Fluid Dynamics Research, Vol. 26 (2) (2000) pp. 69-94
© 1999 Elsevier Science B.V. All rights reserved.
PII: S0169-5983(99)00015-5

Unsteady viscous flow about a submerged circular cylinder with a steady current

B. Yan

School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK

Received 11 January 1999; received in revised form 22 March 1999

Abstract

Viscous flow about a submerged circular cylinder, which oscillates in an otherwise steady current, is considered. The amplitude of the oscillation is assumed small compared with the dimension of the cylinder and the magnitude of the oscillation generated velocity is comparable with that of the steady current. Attention is mainly paid to the influence of the steady current upon the induced steady streaming. It is demonstrated that when the magnitude of the steady current is relatively large the induced steady streaming for rectilinear oscillations is largely independent of the type of oscillation. However, when the magnitude of the steady current is small, the Reynolds stresses produced by the oscillation become significant in the neighbourhood of the cylinder and hence the induced steady streaming is of the classic four-cell structure. When the cylinder performs uniform orbital motion, the circulation around the cylinder due to the induced steady streaming is almost independent of the magnitude of the steady current.

Keywords: Steady current; Steady streaming; Free surface; Forces; Oscillating cylinder

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