Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T04:59:27.573Z Has data issue: false hasContentIssue false
  • English
  • Français

On the flow downstream of separation in an incompressible fluid

Published online by Cambridge University Press:  24 October 2008

K. Stewartson
K. Stewartson
Affiliation:
Department of MathematicsUniversity of Bristol
Get access Rights & Permissions [Opens in a new window]

Extract

When a stream is flowing along a wall against an adverse pressure gradient, the skin friction at the wall decreases to zero, at which point or at least very near it the flow seems to leave the surface altogether. Between the main stream and the wall there may be a slow back-flow. Upstream of separation the influence of the wall on the flow is satisfactorily explained by the boundary-layer theory, which among other things presupposes that this influence is confined to a narrow region near the wall. Such a theory is clearly inadequate downstream, however, because this layer rapidly increases in width and, further, the main stream is seriously affected, and consideration of the Navier-Stokes equations would seem to be necessary before a full theoretical explanation of separation could be given. Apart from a note by Dean (2) on the relations between the pressure and velocity at separation, there has, however, been no relevant attack on these equations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 3 , July 1953 , pp. 561 - 569
Copyright
Copyright © Cambridge Philosophical Society 1953

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)Carrier, G. F. and Lin, C. C.Quart. appl. Math. 6 (1948), 63.CrossRefGoogle Scholar
(2)Dean, W. R.Proc. Camb. phil. Soc. 46 (1950), 293.CrossRefGoogle Scholar
(3)Goldstein, S. (ed.). Modern developments in fluid dynamics (Oxford, 1938), p. 422.Google Scholar
(4)Goldstein, S.Quart. J. Mech. 1 (1948), 43.CrossRefGoogle Scholar
(5)Jones, C. W.Quart. J. Mech. 1 (1948), 385.CrossRefGoogle Scholar
(6)Lighthill, M. J.Proc. roy. Soc. A (to be published).Google Scholar