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Spatial stability of the non-parallel Bickley jet

Published online by Cambridge University Press:  20 April 2006

Vijay K. Garg
Vijay K. Garg
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kanpur
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Abstract

The spatial stability of the plane, two-dimensional jet flow to infinitesimal disturbances is investigated by taking into account the effects of transverse velocity component and the streamwise variations of the basic flow and of the disturbance amplitude, wave-number and spatial growth rate. This renders the growth rate dependent on the flow variable as well as on the transverse and streamwise co-ordinates. Growth rates for the energy density of the disturbance and the associated neutral curves are provided as a function of the streamwise co-ordinate. Variation of growth rate of the disturbance stream function and streamwise component of velocity with the transverse co-ordinate is also given for different disturbance frequencies and streamwise locations. Results are compared with those for the parallel-flow stability analysis, and also with those for an analysis that accounts for only some of the non-parallel effects. It is found that the critical Reynolds number based on the growth of energy density of the disturbance depends on the streamwise co-ordinate and lies within the range (around 20) found experimentally, while the parallel-flow theory yields a rather low value of 4·0.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 102 , January 1981 , pp. 127 - 140
Copyright
© 1981 Cambridge University Press

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References

Bajaj, A. K. & Garg, V. K. 1977 J. Appl. Mech. 44, 378.
Barry, M. D. J. & Ross, M. A. S. 1970 J. Fluid Mech. 43, 813.
Bouthier, M. 1972 J. Mec. 11, 599.
Bouthier, M. 1973 J. Mec. 12, 75.
Clenshaw, C. W. & Elliot, D. A. 1960 Quart. J. Mech. Appl. Math. 13, 300.
Crighton, D. G. & Gaster, M. 1976 J. Fluid Mech. 77, 397.
Curle, N. 1957 Proc. Roy. Soc. A 238, 489.
Eagles, P. M. 1977 Proc. Roy. Soc. A 355, 209.
Eagles, P. M. & Weissman, M. A. 1975 J. Fluid Mech. 69, 241.
Gaster, M. 1974 J. Fluid Mech. 66, 465.
Haaland, S. E. 1972 Ph.D. thesis, University of Minnesota, Minneapolis.
Hildebrand, F. B. 1974 Introduction to Numerical Analysis, 2nd edn. McGraw-Hill.
Ling, C. H. & Reynolds, W. C. 1973 J. Fluid Mech. 59, 571.
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, vol. I, p. 139. Massachusetts Institute of Technology Press.
Saric, W. S. & Nayfeh, A. H. 1975 Phys. Fluids 18, 945.
Sato, H. & Sakao, F. 1964 J. Fluid Mech. 20, 337.
Shen, S. F. 1961 J. Aero. Sci. 28, 397.
Smith, F. T. 1979 Proc. Roy. Soc. A 366, 91.
Tatsumi, T. & Kakutani, T. 1958 J. Fluid Mech. 4, 261.