Burgers flow past arbitrary ellipse
Author:
J. M. Dorrepaal
Journal:
Quart. Appl. Math. 42 (1985), 497-512
MSC:
Primary 76D99; Secondary 35Q10, 35Q20
DOI:
https://doi.org/10.1090/qam/766885
MathSciNet review:
766885
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Abstract: This paper examines a linearization of the Navier-Stokes equation due to Burgers in which vorticity is transported by the velocity field corresponding to continuous potential flow. The governing equations are solved exactly for the two dimensional steady flow past an ellipse of arbitrary aspect ratio. The requirement of no slip along the surface of the ellipse results in an infinite algebraic system of linear equations for coefficients appearing in the solution. The system is truncated at a point which gives reliable results for Reynolds numbers $R$ in the range $0 < R \le 5$.
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D. J. Tritton, Experiments on the flow past a circular cylinder at low Reynolds numbers, J. Fluid Mech. 6, 547–567 (1959)
L. A. Skinner, Generalized expansions for slow flow past a cylinder, Quart. J. Mech. Appl. Math. 28, 333–340 (1975)
M. Van Dyke, Perturbation methods in fluid mechanics, Parabolic Press, Stanford, California 1975, p. 236
J. M. Burgers, Oseen’s theory for the approximate determination of the flow of a fluid with very small friction along a body, Proc. Acad. Sci. Amsterdam 31, 433–453 (1928)
H. L. Dryden, F. D. Murnaghan and H. Bateman, Hydrodynamics, Dover Publications, New York, 1956, pp. 265–266
N. W. McLachlan, Theory and application of Mathieu functions, Dover Publications, New York, 1964, pp. 10, 22, 369
I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and products, Academic Press, New York, 1965, pp. 42, 971
H. Yamada, On the slow motion of viscous liquid past a circular cylinder, Rep. Res. Inst. Appl. Mech. Kyushu Univ. 3, 11–23 (1954)
R. L. Underwood, Calculation of incompressible flow past a circular cylinder at moderate Reynolds numbers, J. Fluid Mech. 37, 95–114 (1969)
I. Imai, On the asymptotic behaviour of viscous fluid flow at a great distance from a cylindrical body with special reference to Filon’s paradox, Proc. Roy. Soc. Ser. A 208, 487–516 (1951)
M. Kawaguti, Numerical solution of the Navier-Stokes equations for the flow around a circular cylinder at Reynolds number 40, J. Phys. Soc. Japan 8, 747–757 (1953)
S. C. R. Dennis and J. Dunwoody, The steady flow of a viscous fluid past a flat plate, J. Fluid Mech. 24, 577–595 (1966)
W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and theorems for the special functions of mathematical physics, Springer-Verlag Inc., New York, 1966, p. 469
D. J. Tritton, Experiments on the flow past a circular cylinder at low Reynolds numbers, J. Fluid Mech. 6, 547–567 (1959)
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Article copyright:
© Copyright 1985
American Mathematical Society
