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Drift

Published online by Cambridge University Press:  28 March 2006

M. J. Lighthill
M. J. Lighthill
Affiliation:
Department of Mathematics, University of Manchester
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Abstract

Sir Charles Darwin has advocated a study of the ‘drift’ of material surfaces in the classically investigated irrotational flows past bodies. This suggestion is followed up and given further support in the present paper. In particular, it is shown how secondary flows can be evaluated by use of the ‘drift function’ t for the primary flow. This is a function (§1) such that material surfaces initially at right angles to the stream drift into shapes expressible by equations t=constant.

The analysis leads to a simple expression (§4) for the secondary velocity field in the flow past an infinite cylinder of any cross-section, with the upstream velocity normal to its axis and increasing linearly with distance along the axis-a problem in which only the secondary vorticity field was previously known. The drift past a sphere is computed and illustrated (§6), and the secondary vorticity field in shear flow past a sphere is tabulated (§7). There is also a detailed study (§3) of the asymptotic form of the secondary velocity field in flow past any body, based on a result of Darwin concerning ‘hydrodynamic mass’.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 1 , Issue 1 , May 1956 , pp. 31 - 53
Copyright
© 1956 Cambridge University Press

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References

Darwin, C. G. 1953 Proc. Camb. Phil. Soc. 49, 342.
Hawthorne, W. R. 1951 Proc. Roy. Soc. A, 206, 374.
Hawthorne, W. R. 1954 J. Aero. Sci. 21, 588.
Hawthorne, W. R. & Martin, Moira E. 1955 Proc. Roy. Soc. A, 232, 184.
Lighthill, M. J. 1956 Proc. Camb. Phil. Soc. 52, 317.
Taylor, G. I. 1928 Proc. Roy. Soc. A, 120, 13.
Young, A. D. & Maas, J. N. 1936 Aero. Res. Counc., Lond., Rep. & Mem. no. 1770.