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Finite disturbances and growing vortices in a two-dimensional jet

Published online by Cambridge University Press:  11 April 2006

Motoyoshi Ikeda
Motoyoshi Ikeda
Affiliation:
Institute of Space and Aeronautical Science, University of Tokyo, Japan
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Abstract

Disturbances in a two-dimensional jet of a viscous incompressible fluid are examined for the case where the jet has a parabolic velocity distribution at the nozzle mouth. Partial differential equations for a finite amplitude disturbance are solved by use of the finite-difference approximation, in which case the jet is analogous to that excited externally. Numerical calculations for various disturbance amplitudes clarify the nonlinearity of the solution. Moreover, the behaviour of the finite disturbance is compared with the behaviour of an infinitesimal disturbance determined from a linearized stability theory. Streaklines calculated from the finite amplitude solution indicate ‘rolling-up’. The computations are carried out over the range of jet Reynolds numbers 500-2000.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 80 , Issue 3 , 2 May 1977 , pp. 401 - 421
Copyright
© 1977 Cambridge University Press

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References

Abernathy, F. H. & Kronauer, R. E. 1962 J. Fluid Mech. 13, 1.
Anderson, A. B. C. 1954 J. Acoust. Soc. Am. 26, 21.
Anderson, A. B. C. 1955 J. Acoust. Soc. Am. 27, 13.
Anderson, A. B. C. 1956 J. Acoust. Soc. Am. 27, 1048.
Beavers, G. S. & Wilson, T. A. 1970 J. Fluid Mech. 44, 97.
Becker, H. A. & Massaro, T. A. 1968 J. Fluid Mech. 31, 435.
Browand, F. K. 1966 J. Fluid Mech. 26, 281.
Fromm, J. E. & Harlow, F. H. 1963 Phys. Fluids, 6, 975.
Gill, A. E. 1962 J. Fluid Mech. 14, 557.
Griffin, O. M. & Votaw, C. W. 1972 J. Fluid Mech. 51, 31.
Hama, F. R. 1962 Phys. Fluids, 5, 644.
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Michalke, A. 1965 J. Fluid Mech. 23, 521.
Miksad, R. W. 1973 J. Fluid Mech. 59, 1.
Mollendorf, J. C. & Gebhart, B. 1973 J. Fluid Mech. 61, 367.
Pekeris, C. L. & Shkoller, B. 1969 J. Fluid Mech. 39, 629.
Roache, P. J. & Mueller, T. J. 1970 A.I.A.A. J. 8, 530.
Rosenhead, L. 1931 Proc. Roy. Soc. A 134, 170.
Sato, H. 1960 J. Fluid Mech. 7, 53.
Watson, J. 1962 J. Fluid Mech. 14, 211.
Zabusky, N. J. & Deem, G. S. 1971 J. Fluid Mech. 47, 353.