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The Hagen–Poiseuille linear flow instability


In this study, it is shown that the linear instability of the Hagen–Poiseuille (HP) flow for the finite Reynolds numbers Re > Re th is nevertheless possible but only under the condition of refusal to use the traditional “normal” form of disturbances.

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  1. O. Reynolds, Proc. Roy. Soc. London 35, 84 (1883).

    Article  Google Scholar 

  2. D. Joseph, Stability of Fluid Motions (Springer, Berlin, 1976).

    Google Scholar 

  3. P. G. Drazin and N. H. Reid, Hydrodynamic Stability (Cambridge: Cambridge Univ. Press, 1981).

    MATH  Google Scholar 

  4. L. D. Landau and E. M. Lifshitz, Theoretical Physics: Hydrodynamics (Moscow, 2006) [in Russian].

    Google Scholar 

  5. S. Grossman, Rev. Mod. Phys. 72 (2), 603 (2000).

    ADS  Article  Google Scholar 

  6. R. Fitzegerald, Phys. Today 57 (2), 21 (2004).

    Article  Google Scholar 

  7. H. Faisst and B. Eckhardt, Phys. Rev. Lett. 91 (22), 224502 (2003).

    ADS  Article  Google Scholar 

  8. H. Wedin and R. Kerswell, Fluid Mech. 508, 333 (2004).

    MathSciNet  ADS  Article  MATH  Google Scholar 

  9. W. Pfenniger, in Boundary Layer and Flow Control (Pergamon, Oxford, 1961), Vol. 2, p. 970.

    Google Scholar 

  10. J. A. Fox, M. Lessen, and W. V. Bhat, Phys. Fluids 11 (1), 1 (1968).

    ADS  Article  Google Scholar 

  11. S. G. Chefranov and A. G. Chefranov, Zh. Eksp. Teor. Fiz. 146 (2), 373 (2014).

    MathSciNet  Google Scholar 

  12. G. Z. Gershuni, Soros. Obrazovat. Zhurn. Fizika, No. 2, 99 (1997).

    Google Scholar 

  13. G. B. Schubauer and H. K. Skramstad, J. Aeronaut. Sci. 14 (2), 69 (1947).

    Article  Google Scholar 

  14. S. G. Chefranov, JETP Lett. 73 (6), 274 (2001).

    ADS  Article  Google Scholar 

  15. G. Lamb, Hydrodynamics (Moscow, Leningrad, 1947) [in Russian].

    Google Scholar 

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Correspondence to S. G. Chefranov.

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Original Russian Text © S.G. Chefranov, A.G. Chefranov, 2015, published in Doklady Akademii Nauk, 2015, Vol. 463, No. 3, pp. 286–292.

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Chefranov, S.G., Chefranov, A.G. The Hagen–Poiseuille linear flow instability. Dokl. Phys. 60, 327–332 (2015).

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  • Reynolds Number
  • DOKLADY Physic
  • Flow Instability
  • Energy Method
  • Tube Axis