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On the viscous modes of instability of a trailing line vortex

Published online by Cambridge University Press:  26 April 2006

Mehdi R. Khorrami
Mehdi R. Khorrami
Affiliation:
Department of Mechanical Engineering and Mechanics, Old Dominion University, Norfolk, VA 23529-0247, USA Present address: High Technology Corporation, 28 Research Drive, Hampton, VA 23666, USA.
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Abstract

A viscous linear stability analysis of a trailing line (Batchelor) vortex is presented. Employing a staggered Chebyshev spectral collocation technique, very accurate results were obtained. The destabilising role of viscous forces has been shown to produce two types of viscous instability modes. These viscous disturbances consist of an axisymmetric mode and an asymmetric mode. Both disturbances are long-wave instabilities with maximum growth rates which are orders of magnitude smaller than the inviscid modes which have been found by others. Comparison with experimental results and condensation trail observations are found to be in good qualitative agreement with the present study.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 225 , April 1991 , pp. 197 - 212
Copyright
© 1991 Cambridge University Press

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References

Batchelor, G. K.: 1964 J. Fluid Mech. 20, 645–658.
Batchelor, G. K. & Gill, A. E., 1962 J. Fluid Mech. 14, 529–552.
Bisgood, P. L.: 1980 Some observations of condensation trails. Rl Aircraft Establishment TM FS 330.Google Scholar
Crow, S. C.: 1970 AIAA J. 8, 2172–2179.
Crow, S. C. & Champagne, F. H., 1971 J. Fluid Mech. 48, 547–591.
Duck, P. W.: 1986 Z. Angew. Math. Phys. 37, 340–360.
Duck, P. W. & Foster, M. R., 1980 Z. Angew. Math. Phys. 31, 523–530.
Foster, M. R. & Duck, P. W., 1982 Phys. Fluids 25, 1715–1718.
Gottlieb, D., Hussaini, M. Y. & Orszag, S. A., 1984 Theory and applications of spectral methods. In Spectral Methods for Partial Differential Equations (ed. R. G. Voight, D. Gottlieb & M. Y. Hussaini). Philadelphia: Soc. Indus. & Appl. Maths.
Gottlieb, D. & Orszag, S. A., 1977 Numerical Analysis of Spectral Methods: Theory and Applications. Philadelphia: Soc. Indus. & Appl. Maths.
Ho, C.-M. & Huerre, P. 1984 Ann. Rev. Fluid Mech. 16, 365–424.
Ito, T., Suematsu, Y. & Hayase, T., 1985 Mem. Faculty of Engng, Nagoya University 37, 117–172.
Khorrami, M. R.: 1989 A study of the temporal stability of multiple cell vortices. Ph.D. dissertation, Old Dominion University (NASA Contractor Rep. 4261).
Khorrami, M. R.: 1991 Intl J. Numer. Methods Fluids 12 (to appear).
Khorrami, M. R., Malik, M. R. & Ash, R. L., 1989 J. Comput. Phys. 81, 206–229.
Leibovich, S. & Stewartson, K., 1983 J. Fluid Mech. 126, 335–356.
Lessen, M. & Paillet, F., 1974 J. Fluid Mech. 65, 769–779.
Lessen, M., Singh, P. J. & Paillet, F., 1974 J. Fluid Mech. 63, 753–763.
Maslowe, S. A. & Stewartson, K., 1982 Phys. Fluids 25, 1517–1523.
Sarpkaya, T.: 1983 J. Fluid Mech. 136, 85–109.
Sarpkaya, T. & Daly, J. J., 1987 AIAA J. Aircraft 24, 399–04.
Singh, P. I. & Uberoi, M. S., 1976 Phys. Fluids 19, 1858–1863.
Staley, D. O. & Gall, R. L., 1984 J. Atmos. Sci. 41, 422–429.
Stewartson, K.: 1982 Phys. Fluids 1953–1957.
Stewartson, K. & Brown, S. N., 1985 J. Fluid Mech. 156, 387–399.
Stewartson, K. & Capell, K., 1985 J. Fluid Mech. 156, 369–386.
Stewartson, K. & Leibovich, S., 1987 J. Fluid Mech. 178, 549–566.
Strange, C. & Harvey, J. K., 1983 Instabilities in trailing vortices: flow visualization using hotwire anemometry. AGARD-CP–342.Google Scholar
Wilkinson, J. H.: 1965 The Algebraic Eigenvalue Problem. Oxford University Press.