A weak momentum source in a uniform stream
Author:
D. R. Breach
Journal:
Quart. Appl. Math. 28 (1970), 427-431
DOI:
https://doi.org/10.1090/qam/99782
MathSciNet review:
QAM99782
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Abstract: The interaction of a momentum source with a viscous uniform stream is studied. Taken separately, each flow is described by an exact solution of the full Navier-Stokes equations. Their combined effect can be described in terms of two non-dimensional parameters related to the strength of the source and the distance from it. A perturbation solution for the case of a weak source is attempted and the initial terms are found. It is shown that the results are closely related to the Oseen expansion for viscous streaming past a spheroid and that when the momentum of the source opposes that of the stream a closed streamline of elliptical shape is formed.
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D. R. Breach, Slow flow past ellipsoids of revolution, J. Fluid Mech. 10, 306–314 (1961)
S. Goldstein, The steady flow of a viscous fluid past a fixed spherical obstacle at small Reynolds numbers, Proc. Roy. Soc. London A123, 225–235 (1929)
L. D. Landau, A new exact solution of Navier-Stokes equations, Dokl. Akad. Nauk SSSR 43, 286–288 (1944)
L. D. Landau and E. M. Lifshitz, Fluid mechanics, 2nd ed., GITTL, Moscow, 1953; English transl., Pergamon Press, New York and Addison-Wesley, Reading, Mass., 1959
I. Proudman and J. R. A. Pearson, Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder, J. Fluid Mech. 2, 237–262 (1957)
L. I. Sedov, Similarity and dimensional methods in mechanics, GITTL, Moscow, 1957; English transl. of 4th ed., Academic Press, New York, 1959
H. B. Squire, The round laminar jet, Quart. J. Mech. Appl. Math. 4, 321–329 (1951)
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Article copyright:
© Copyright 1970
American Mathematical Society
