A conformally invariant Oseen equation for flow at small Reynolds numbers
Author:
K. B. Ranger
Journal:
Quart. Appl. Math. 48 (1990), 189-199
MSC:
Primary 76D05; Secondary 35Q53
DOI:
https://doi.org/10.1090/qam/1040242
MathSciNet review:
MR1040242
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Abstract: Starting from a complex variable formulation of the exact Navier-Stokes equations for the steady two-dimensional motion of an incompressible viscous fluid, a Burgers type linearization is introduced at small Reynolds number which results in a conformally invariant Oseen equation. The independent variables are the velocity potential and stream function for the corresponding irrotational flow. There are certain analytical advantages in this approach for the determination of uniformly valid approximations to flow at small Reynolds numbers and the method is illustrated by various examples.
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G. B. Jeffery, The rotation of two circular cylinders in a viscous fluid, Proc. Roy. Soc. London A101, 169–174 (1922)
J. Wilkinson, A note on the Oseen approximation for a paraboloid in a uniform stream parallel to its axis, Quart. J. Mech. Appl. Math. 8, 415–421 (1955)
J. A. Lewis and G. F. Carrier, Some remarks on the flat plate boundary layer Quart. Appl. Math. 7 228–234,(1949)
H. L. Dryden, F. P. Murnaghan, and H. Bateman, Hydrodynamics, Dover, New York, 1956, (a) pp. 233–235, (b) pp. 265–266
R. Legendre, Solution plus complète du problème Blasius, Comptes Rendus 228, June 1949, 2008-2010
D. E. R. Godfrey, Theoretical Elasticity and Plasticity for Engineers, Thames and Hudson, London, 1959, pp. 58–59
G. B. Jeffery, The rotation of two circular cylinders in a viscous fluid, Proc. Roy. Soc. London A101, 169–174 (1922)
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Article copyright:
© Copyright 1990
American Mathematical Society
