Abstract
It is shown by a numerical calculation that the Malkus hypothesis regarding the neutral stability of the average velocity profile of a turbulent flow with respect to external perturbations is invalid.
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W. V. Malkus, “Outline of a thoery of turbulent shear flow,” J. Fluid Mech.,1, Pt. 5, 521 (1956).
A. A. Townsend, “Remarks on the Malkus theory of turbulent flow,” Collog. Internat. Centre Nat. Rech. Sci., No. 108, 167–180 (1962).
E. A. Spiegel, “On the Malkus theory of turbulence,” Collog. Internat. Centre Nat. Rech. Sci., No. 108, 181–199 (1962).
J. C. J. Nihoul, “Hamiltonian description of irreversible stationary phenomena and elements of a turbulence theory,” J. Mechanique,6, No. 3 (1967).
S. Savelescu and A. Nastase, “Theoretical derivation of the turbulent velocity profile on the basis of the minimum of the total energy of the oscillations,” Wiss. Z. Tech. Univ. Dresden,16, No. 4 (1967).
W. C. Reynolds and W. G. Tiederman, “Stability of turbulent channel flow with application to the Malkus theory,” J. Fluid Mech.,27, Pt. 2 (1967).
J. C. J. Nihoul, “Tentative Lagrangian for the determination of the mean velocity profile in turbulent channel flow by a Hamiltonian principle,” Z. Angew. Math. und Mech.,48, No. 8 (1968).
J. C. J. Nihoul, “On a principle of minimum Reynolds number and the Malkus theory of turbulent channel flow,” Bull. Soc. Roy. Sci. Liège,38, No. 3, 4 (1969).
Head and Mass Transfer and Friction in a Turbulent Boundary Layer [in Russian], Izd. SO AN SSSR, Novosibirsk (1964).
E. R. Van Driest, “On turbulent flow near a wall,” J. Aeronaut. Sci.,23, No. 11 (1956).
A. S. Monin and A. M. Yaglom, Statistical Hydromechnics, Pt. 1 [in Russian], Nauka, Moscow (1965).
M. A. Gol'dshtik, and V. A. Sapozhnikov, “Stability of laminar flow in the presence of a field of mass forces,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 5 (1968).
M. A. Gol'dshtik, V. A. Sapozhnikov, and V. N. Shtern, “Local properties of the problem of hydrodynamical stability,” Zh. Prikl. Mekhan. i Tekh. Fiz., No. 2 (1970).
M. A. Gol'dshtik, “Principle of maximum stability of average turbulent flows,” Dokl. Akad. Nauk SSSR,182, No. 5 (1968).
M. A. Gol'dshtik and S. S. Kutateladze, “Calculation of the constant of boundary-layer turbulence,” Dokl. Akad. Nauk SSSR,185, No. 3 (1969).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 172–176, September–October, 1970.
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Gol'dshtik, M.A., Sapozhnikov, V.A. & Shtern, V.N. Verification of the Malkus hypothesis regarding the stability of turbulent flows. Fluid Dyn 5, 863–867 (1970). https://doi.org/10.1007/BF01017309
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DOI: https://doi.org/10.1007/BF01017309