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Instability of the two-dimensional Poiseuille flow between elastic plates

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Abstract

The pressure-driven Poiseuille flow of a viscous incompressible fluid between two parallel plates is considered. Within the framework of the triple-deck theory, the elasticity of the walls is shown to have a stabilizing effect on the flow.

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References

  1. A. V. Boiko, G. R. Grek, A. V. Dovgal, and V. V. Kozlov, The Origin of Turbulence in Near-Wall Flows (Nauka, Ross. Akad. Nauk, Novosibirsk, 1999; Berlin, Springer-Verlag, 2002).

    Google Scholar 

  2. V. Ya. Neiland, “Towards a Theory of Separation of the Laminar Boundary Layer in a Supersonic Stream,” Izv. Akad. Nauk SSSR. Mekh. Zhidk. Gaza, No. 4, 53–58 (1969).

  3. K. Stewartson and P. G. Williams, “Self-Induced Separation,” Proc. R. Soc. London, Ser. A 312(1509), 181–206 (1969).

    Article  MATH  Google Scholar 

  4. A. F. Messiter, “Boundary-Layer Flow near the Trailing Edge of a Flat Plate,” SIAM J. Appl. Math. 18, 241–257 (1970).

    Article  MATH  Google Scholar 

  5. I. V. Savenkov, “The Suppression of the Growth of Nonlinear Wave Packets by the Elasticity of the Surface around Which Flow Occurs,” Comput. Math. Math. Phys. 35, 73–79 (1995).

    MATH  MathSciNet  Google Scholar 

  6. I. V. Savenkov, “Effect of Surface Elasticity on Boundary-Layer Stability for Transonic Free-Stream Velocities,” Comput. Math. Math. Phys. 41, 130–135 (2001).

    MATH  MathSciNet  Google Scholar 

  7. I. V. Savenkov, “Effect of Surface Elasticity on the Transformation of Acoustic Disturbances into Tollmien-Schlichting Waves in a Boundary Layer at Transonic Free-Stream Velocities,” Comput. Math. Math. Phys. 46, 907–913 (2006).

    Article  MathSciNet  Google Scholar 

  8. I. V. Savenkov, “Three-Dimensional Tollmien-Schlichting Waves Generated by Sound in the Boundary Layer on an Elastic Surface at Transonic Free-Stream Velocities,” Comput. Math. Math. Phys. 47, 510–517 (2007).

    Article  MathSciNet  Google Scholar 

  9. V. I. Zhuk and O. S. Ryzhov, “Free Interaction of Near-Wall Layers with the Poiseuille Flow Core,” Dokl. Akad. Nauk SSSR 257, 55–59 (1981).

    MathSciNet  Google Scholar 

  10. E. V. Bogdanova and O. S. Ryzhov, “On Oscillations Excited by a Harmonic Oscillator in the Poiseuille Flow,” Dokl. Akad. Nauk SSSR 257, 837–841 (1981).

    Google Scholar 

  11. F. T. Smith, “On the High Reynolds Number Theory of Laminar Flows,” IMA J. Appl. Math. 28, 207–281 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  12. O. S. Ryzhov and E. D. Terent’ev, “Transient Regime Characterizing the Startup of a Vibrator in a Subsonic Boundary Layer on a Plate,” Prikl. Mat. Mekh. 50, 974–986 (1986).

    Google Scholar 

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Correspondence to I. V. Savenkov.

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Original Russian Text © I.V. Savenkov, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 12, pp. 2288–2295.

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Savenkov, I.V. Instability of the two-dimensional Poiseuille flow between elastic plates. Comput. Math. and Math. Phys. 51, 2155–2161 (2011). https://doi.org/10.1134/S0965542511120177

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