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On the flow near the trailing edge of a flat plate II

Published online by Cambridge University Press:  26 February 2010

K. Stewartson
K. Stewartson
Affiliation:
University College, London
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Extract

Consider an incompressible fluid of density p and kinematic viscosity v in an infinite two-dimensional domain. We assume that the fluid has a uniform velocity U∞, in the direction of the positive x*-axis of a rectangular Cartesian coordinate system Ox* y*, at large distances from a fixed flat plate of zero thickness which occupies the interval −l < x* < 0 of the line Ox*. Of special interest here is the structure of the flow when ε ≪ 1 where

Re being the Reynolds number of the flow. A first examination was made by Blasius (1908), using Prandtl's theory of the boundary layer, who found inter alia that the leading term of the drag D on one side of the plate is given by

the numerical factor being determined by Goldstein (1930).

Type
Research Article
Information
Mathematika , Volume 16 , Issue 1 , June 1969 , pp. 106 - 121
Copyright
Copyright © University College London 1969

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References

1.Blasius, H., Z. Math. Phys., 56 (1908), 1.Google Scholar
2.Dennis, S. C. R. and Cheng, G-Zu, (1969): to appear in Physics of Fluids.Google Scholar
3.Goldburg, A. and Cheng, Sin-I, J. Math. Mech., 10 (1961), 529.Google Scholar
4.Goldstein, S., Proc. Cambridge Phil. Soc., 26 (1930), 1.Google Scholar
5.Hakkinen, R. J. and O'Neil, E. J., (1967) Rep. DAC-60862, Douglas Aircraft Company, Los Angeles, California.Google Scholar
6.Hakkinen, R. J. and Rott, N., AIAA J., 3 (1965), 1553.CrossRefGoogle Scholar
7.Lighthill, M. J., Proc. Roy. Soc. Ser. A., 217 (1953), 478.Google Scholar
8.Messiter, A. F. (1969), to appear in SIAM J. of Applied Math.Google Scholar
9.Prandtl, L. (1905) Verh. Ill Internat. Math. Kongr. Heidelberg (Teubner, Leipzig), 484.Google Scholar
10.Stewartson, K., Proc. Roy. Soc. Ser. A., 306 (1968), 275.Google Scholar
11.Stewartson, K. and Williams, P. G. (1969) to appear in Proc. Roy. Soc. Ser. A.Google Scholar
12.Van Dyke, M. D.Perturbation methods in fluid mechanics (Academic Press, 1964), 136.Google Scholar