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Steady streaming induced between oscillating cylinders

Published online by Cambridge University Press:  19 April 2006

P. W. Duck  and
F. T. Smith
P. W. Duck
Affiliation:
Department of Mathematics, Imperial College, London Present address: Department of Aeronautical and Astronautical Engineering, Ohio State University, Columbus, Ohio 43210.
F. T. Smith
Affiliation:
Department of Mathematics, Imperial College, London
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Abstract

The flow of an incompressible fluid contained between two infinitely long circular cylinders is considered when the inner cylinder performs small harmonic oscillations about the centre of the larger (fixed) cylinder. Numerical solutions are presented for the Navier–Stokes equations governing the steady-streaming component of the motion. Special attention is then paid to this flow when the Reynolds number of the steady streaming is large, and when the radius of the outer cylinder is much larger than that of the inner. Results obtained show an improved correlation with experimental results and indicate strongly that the finiteness of the domain is the major cause of the discrepancies between experiment and previous theoretical studies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 91 , Issue 1 , 9 March 1979 , pp. 93 - 110
Copyright
© 1979 Cambridge University Press

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References

Batchelor, G. K. 1956 J. Fluid Mech. 1, 177.
Bertelsen, A. F. 1974 J. Fluid Mech. 64, 589.
Bertelsen, A. F., Svardal, A. & Tjotta, S. 1973 J. Fluid Mech. 59, 493.
Bickley, W. G. 1937 Phil. Mag. 23, 727.
Davidson, B. J. & Riley, N. 1972 J. Fluid Mech. 53, 287.
Goldstein, S. 1930 Proc. Camb. Phil. Soc. 26, 1.
Holtsmark, J., Johnsen, I., Sikkeland, T. & Skavlem, S. 1954 J. Acoust. Soc. Am. 26, 26.
Lyne, W. H. 1971 J. Fluid Mech. 45, 13.
McConalogue, D. J. & Srivastava, R. S. 1968 Proc. Roy. Soc. A 307, 37.
Riley, N. 1965 Mathematika 12, 161.
Riley, N. 1967 J. Inst. Math. Appl. 3, 419.
Riley, N. 1975 J. Fluid Mech. 68, 801.
Segel, L. A. 1961 Quart. Appl. Math. 18, 335.
Skavlem, S. & Tjøtta, S. 1955 J. Acoust. Soc. Am. 27, 26.
Smith, F. T. 1974 J. Inst. Math. Appl. 13, 127.
Smith, F. T. 1977 Proc. Roy. Soc. A 356, 443.
Smith, F. T. & Duck, P. W. 1977 Quart. J. Mech. Appl. Math. 30, 143.
Stewartson, K. 1958 Proc. Symp. P.L. Res. Freiburg i. Br., 1957, pp. 57–91. Springer.
Stewartson, K. 1970 J. Fluid Mech. 44, 347.
Stuart, J. T. 1963 In Laminar Boundary Layers, chap. 7. Oxford University Press.
Stuart, J. T. 1966 J. Fluid Mech. 24, 673.
Sychev, V. Ya. 1972 Izv. Akad. Nauk SSSR, Mekh. Zh. Gaza 3, 47.
Wang, C. Y. 1968 J. Fluid Mech. 32, 55.