Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T14:28:07.013Z Has data issue: false hasContentIssue false
  • English
  • Français

The growth of secondary circulation in frictionless flow

Published online by Cambridge University Press:  24 October 2008

W. R. Hawthorne
W. R. Hawthorne
Affiliation:
Department of EngineeringUniversity of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

The appearance of a component of vorticity in the direction of flow materially alters the pattern of flow of a fluid in three dimensions. Expressions are obtained for this secondary vorticity in an inviscid compressible fluid flowing under the action of body forces. They are applied to examples such as a liquid under gravity and gas flow behind a curved shock. In compressible gas flow with varying temperature but constant stagnation pressure no secondary circulation appears. In a perfect gas atmosphere it is shown that secondary circulation may appear because of nou-adiabatic lapse rates as well as wind-speed gradients. It is also shown that in a liquid with a density gradient, gravitational effects can give rise to secondary vorticity components.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 4 , October 1955 , pp. 737 - 743
Copyright
Copyright © Cambridge Philosophical Society 1955

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

REFERENCES

(1)Detra, R. W.Mitt. Inst. Aerodyn. Zürich, no. 20 (1953).Google Scholar
(2)Ehrich, F. F.J. aero. Sci. 22 (1955), 51.CrossRefGoogle Scholar
(3)Eichenberger, H. P.J. Math. Phys. 32 (1953), 34.CrossRefGoogle Scholar
(4)Hawthorne, W. R.Proc. roy. Soc. A, 206 (1951), 374.Google Scholar
(5)Hawthorne, W. R.J. aero. Sci. 21 (1954), 588.CrossRefGoogle Scholar
(6)Hawthorne, W. R. and Armstrong, W. D.Quart. J. Mech. 8 (1955), (in the press).Google Scholar
(7)Hunk, M. and Prim, R. C.Proc. nat. Acad. Sci., Wash., 33 (1947), 137.Google Scholar
(8)Squire, H. B. and Winter, K. G.J. aero. Sci. 18 (1951), 271.CrossRefGoogle Scholar
(9)Vazsonyi, A.Quart. appl. Math. 3 (1947), 29.CrossRefGoogle Scholar