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The Hagen–Poiseuille linear flow instability

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Abstract

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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References

  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).

    Article  ADS  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).

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  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).

    Article  ADS  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).

    Article  ADS  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). https://doi.org/10.1134/S1028335815070083

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  • DOI: https://doi.org/10.1134/S1028335815070083

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