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Non-parallel-flow stability of a two-dimensional buoyant plume

Published online by Cambridge University Press:  20 April 2006

Shunichi Wakitani
Shunichi Wakitani
Affiliation:
Department of Mechanical Engineering, University of Osaka Prefecture, Sakai, Osaka 591, Japan
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Abstract

The linear stability of a two-dimensional buoyant plume is analysed by taking into account the transverse velocity component and the streamwise variations of the basic flow and of the disturbance waves. The solutions indicate the dependence of the spatial amplification rate and wavenumber on the disturbance flow quantity under consideration as well as on the streamwise and transverse coordinates. The use of the flow quantity relative to the basic flow leads to close agreement with the neutral curve according to quasi-parallel-stability theory, the usual method for treating nearly parallel flows. However, the amplification rate within an unstable region shows substantial deviation from that predicted by the quasi-parallel theory. The validity of this non-parallel theory is supported by the existing experimental data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 159 , October 1985 , pp. 241 - 258
Copyright
© 1985 Cambridge University Press

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References

Bill, R. G. & Gebhart, B. 1975 The transition of plane plumes. Intl J. Heat Mass Transfer 18, 513–526.Google Scholar
Bouthier, M. 1972 Stabilité linéaire des écoulements presque parallèles. J. Méc. 11, 599–621.Google Scholar
Bouthier, M. 1973 Stabilité linéaire des écoulements presque parallèles. Partie II. La couche limite de Blasius. J. Méc. 12, 75–95.Google Scholar
Dring, R. P. & Gebhart, B. 1969 An experimental investigation of disturbance amplification in external laminar natural convection flow. J. Fluid Mech. 36, 447–464.Google Scholar
Eagles, P. M. & Weissman, M. A. 1975 On the stability of slowly varying flow: the divergent channel. J. Fluid Mech. 69, 241–262.Google Scholar
Forstrom, R. J. & Sparrow, E. M. 1967 Experiments on the buoyant plume above a heated horizontal wire. Intl J. Heat Mass Transfer 10, 321–331.Google Scholar
Fujii, T. 1963 Theory of the steady laminar natural convection above a horizontal line heat source and a point heat source. Intl J. Heat Mass Transfer 6, 597–606.Google Scholar
Garg, V. K. 1981 Spatial stability of the non-parallel Bickley jet. J. Fluid Mech. 102, 127–140.Google Scholar
Garg, V. K. & Round, G. F. 1978 Nonparallel effects on the stability of jet flows. Trans. ASME E: J. Appl. Mech. 45, 717–722.Google Scholar
Gaster, M. 1974 On the effects of boundary-layer growth on flow stability. J. Fluid Mech. 66, 465–480.Google Scholar
Haaland, S. E. 1972 Contributions to linear stability theory of nearly parallel flows. Ph.D. Thesis, University of Minnesota.
Haaland, S. E. & Sparrow, E. M. 1973 Stability of buoyant boundary layers and plumes, taking account of nonparallelism of the basic flows. Trans. ASME C: J. Heat Transfer 95, 295–301.Google Scholar
Hieber, C. A. & Gebhart, B. 1971 Stability of vertical natural convection boundary layers: some numerical solutions. J. Fluid Mech. 48, 625–648.Google Scholar
Hieber, C. A. & Nash, E. J. 1975 Natural convection above a line heat source: higher-order effects and stability. Intl J. Heat Mass Transfer 18, 1473–1479.Google Scholar
Ling, C.-H. & Reynolds, W. C. 1973 Non-parallel flow corrections for the stability of shear flows. J. Fluid Mech. 59, 571–591.Google Scholar
Morris, P. J. 1981 Stability of a two-dimensional jet. AIAA J. 19, 857–862.Google Scholar
Pera, L. & Gebhart, B. 1971 On the stability of laminar plumes: some numerical solutions and experiments. Intl J. Heat Mass Transfer 14, 975–984.Google Scholar
Saric, W. S. & Nayfeh, A. H. 1975 Nonparallel stability of boundary-layer flows. Phys. Fluids 18, 945–950.Google Scholar
Tatsumi, T. & Kakutani, T. 1958 The stability of a two-dimensional laminar jet. J. Fluid Mech. 4, 261–275.Google Scholar
Wakitani, S. & Yosinobu, H. 1984 Stability characteristics of a natural convection flow above a horizontal line heat source. J. Phys. Soc. Japan 53, 1291–1300.Google Scholar
Yosinobu, H., Onishi, Y., Amano, S., Enyo, S. & Wakitani, S. 1979 Experimental study on instability of a natural convection flow above a horizontal line heat source. J. Phys. Soc. Japan 47, 312–319.Google Scholar