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    HOLMES, R. J. HOCKING, G. C. FORBES, L. K. and BAILLARD, N. Y. 2013. Waveless subcritical flow past symmetric bottom topography. European Journal of Applied Mathematics, Vol. 24, Issue. 02, p. 213.


    Hocking, G.C. and Vanden-Broeck, J.-M. 2008. The effect of gravity on flow past a semi-circular cylinder with a constant pressure wake. Applied Mathematical Modelling, Vol. 32, Issue. 5, p. 677.


    ROBB MCDONALD, N. 2008. VORTEX EQUILIBRIA IN FLOW PAST A PLATE. The ANZIAM Journal, Vol. 49, Issue. 03, p. 347.


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Steady Prandtl-Batchelor flows past a circular cylinder

  • G. C. Hocking (a1)
  • DOI: http://dx.doi.org/10.1017/S1446181100003011
  • Published online: 01 February 2009
Abstract
Abstract

The high Reynolds number flow past a circular cylinder with a trailing wake region is considered when the wake region is bounded and contains uniform vorticity. The formulation allows only for a single vortex pair trapped behind the cylinder, but calculates solutions over a range of values of vorticity. The separation point and length of the region are determined as outputs. It was found that using this numerical method there is an upper bound on the vorticity for which solutions can be calculated for a given arclength of the cavity. In some cases with shorter cavities, the limiting solutions coincide with the formation of a stagnation point in the outer flow at both separation from the cylinder and reattachment at the end of the cavity.

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[4]S. Childress , “Solutions of Euler's equations containing finite eddies”, Phys. Fluids 9 (1966) 860872.

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[14]M. J. Lighthill , “On boundary layers and upstream influence, I. A comparison between subsonic and supersonic flows”, Proc. Roy. Soc. Lond. A 217 (1953) 344357.

[15]D. Moore , P. Saffman and S. Tanveer , “The calculation of some Batchelor flows: The Sadovskii vortex and rotational corner flow”, Phys. Fluids 31 (1988) 978990.

[16]V. S. Sadovskii , “Vortex regions in a potential stream with a jump of Bernoulli's constant at the boundary”, Appl. Math. Mech. 35 (1971) 729.

[18]R. V. Southwell and G. Vaisey , “Fluid motions characterised by ‘free’ streamlines”, Phil. Trans. Roy. Soc. A 240 (1946) 117161.

[19]J.-M. Vanden-Broeck , “Nonlinear capillary free-surface flows”, J. Eng. Math. 50 (2004) 415426, Lighthill Memorial Paper.

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The ANZIAM Journal
  • ISSN: 1446-1811
  • EISSN: 1446-8735
  • URL: /core/journals/anziam-journal
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