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Stability of turbulent channel flow, with application to Malkus's theory

  • W. C. Reynolds (a1) and W. G. Tiederman (a2)
Abstract

The Orr-Sommerfeld stability problem has been studied for velocity profiles appropriate to turbulent channel flow. The intent was to provide an evaluation of Malkus's theory that the flow assumes a state of maximum dissipation, subject to certain constraints, one of which is that the mean velocity profile is marginally stable. Dissipation rates and neutral stability curves were obtained for a representative two-parameter family of velocity profiles. Those in agreement with experimental profiles were found to be stable; the marginally stable profile of greatest dissipation was not in good agreement with experiments. An explanation for the apparent success of Malkus's theory is offered.

Copyright
© 1967 Cambridge University Press
References
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Gage, D. H., Schiffer, M., Kline, S. J. & Reynolds, W. C. 1966 The non-existence of a general thermokinetic variational principle. Non-equilibrium Thermodynamics (eds. Donnelly, R. J., Herman, R. & Prigogine, I.). Chicago: University Press.
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Laufer, J. 1951 Investigation of turbulent flow in a two-dimensional channel. NACA Rep. no. 1053.
Lee, L. H. & Reynolds, W. C. 1964 A variational method for investigating the stability of parallel flows. Tech. Rep. no. FM-1, Department of Mechanical Engineering, Stanford University. Stanford, California.
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Malkus, W. V. R. 1956 Outline of a theory of turbulent shear flow J. Fluid Mech. 1, 521.
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Sparrow, E. M. & Siegel, R. 1959 A variational method for fully developed laminar heat transfer in ducts. TASME, Series C, J. Heat Transfer, p. 157.
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Tiederman, W. G. & Reynolds, W. C. 1965 Stability of turbulent Poiseuille flow with application to the Malkus theory of turbulence. Tech. Rep. no. FM-2, Department of Mechanical Engineering, Stanford University. Stanford, California.
Townsend, A. A. 1962 Remarks on the Malkus theory of turbulent flow. Mecanique de la Turbulence, p. 167. Paris: Centre National de la Recherche Scientifique.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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