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Hard excitation of auto-oscillations in a Hagen-Poiseuille flow

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Abstract

Sufficiently powerful perturbations of the flow of a liquid moving in circular pipes results in turbulence, starting with Reynolds numbers of the order of 2200–2300 [1]. It has been established theoretically [2, 3] that the flow of a viscous incompressible liquid in a pipe of circular section (Hagen-Poiseuille flow) is stable with respect to infinitesimally small perturbations for all Reynolds numbers. Attempts to obtain finite-amplitude flow instability by considering only two-dimensional perturbations [4, 5] were also unsuccessful. This paper shows that the considered flow is unstable with respect to three-dimensional perturbations of finite amplitude.

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Literature cited

  1. L. Schiller, Flow of Fluids in Pipes [Russian translation], ONTI NKTP SSSR, Moscow-Leningrad (1936).

    Google Scholar 

  2. H. Salwen and C. E. Grosch, “The stability of Poiseuille flow in a pipe of circular cross-section,” J. Fluid Mech.,54, 93 (1972).

    Google Scholar 

  3. H. Salwen, F. W. Cotton, and C. E. Grosch, “Linear stability of Poiseuille flow in a circular pipe,” J. Fluid Mech.,98, 273 (1980).

    Google Scholar 

  4. N. Itoh, “Nonlinear stability of parallel flows with subcritical Reynolds numbers. Pt. 2. Stability of pipe Poiseuille flow to finite axisymmetric disturbances,” J. Fluid Mech.,82, 469 (1977).

    Google Scholar 

  5. A. T. Patera and S. A. Orszag, “Finite-amplitude stability of axisymmetric pipe flow,” J. Fluid Mech.,112, 467 (1981).

    Google Scholar 

  6. O. A. Ladyzhenskaya, Problems of the Dynamics of a Viscous Incompressible Fluid [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  7. G. I. Petrov, “Application of the Galerkin method to the problem of flow stability for viscous fluid,” Prikl. Mat. Mekh.,4, 3 (1940).

    Google Scholar 

  8. J. A. Fox, M. Lessen, and W. V. Bhat, “Experimental investigation of the stability of Hagen-Poiseuille flow,” Phys. Fluids,11, 1 (1968).

    Google Scholar 

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Authors and Affiliations

  1. Moscow

    N. V. Nikitin

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  1. N. V. Nikitin
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 181–183, September–October, 1984.

The author wishes to express sincere gratitude to G. I. Petrov and S. Ya. Gertsenshtein for their interest in his work.

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Nikitin, N.V. Hard excitation of auto-oscillations in a Hagen-Poiseuille flow. Fluid Dyn 19, 828–830 (1984). https://doi.org/10.1007/BF01093556

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  • DOI: https://doi.org/10.1007/BF01093556

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