Three-dimensional instability of flow in a flat channel between elastic plates. (Russian, English) Zbl 1274.76198

Zh. Vychisl. Mat. Mat. Fiz. 52, No. 10, 1883-1889 (2012); translation in Comput. Math. Math. Phys. 52, No. 10, 1445-1451 (2012).
Summary: The three-dimensional instability of the viscous incompressible flow induced by a pressure gradient between two elastic parallel plates is studied. The triple-deck theory is used to show that the elasticity of the walls has a stabilizing effect on the flow.


76D33 Waves for incompressible viscous fluids
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
Full Text: DOI


[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). · Zbl 1016.76002
[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] Stewartson, K.; Williams, P. G., Self-induced separation, Proc. R. Soc. London, Ser. A, 312, 181-206, (1969) · Zbl 0184.52903
[4] Messiter, A. F., Boundary-layer flow near the trailing edge of a flat plate, SIAM J. Appl. Math., 18, 241-257, (1970) · Zbl 0195.27701
[5] Savenkov, I. V., 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) · Zbl 0842.76028
[6] Savenkov, I. V., Effect of surface elasticity on boundary-layer stability for transonic free-stream velocities, Comput. Math. Math. Phys., 41, 130-135, (2001) · Zbl 1048.35088
[7] Savenkov, I. V., 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)
[8] Savenkov, I. V., 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) · Zbl 1210.76099
[9] Savenkov, I. V., Instability of the two-dimensional Poiseuille flow between elastic plates, Comput. Math. Math. Phys., 51, 2155-2161, (2011) · Zbl 1249.76032
[10] Zhuk, V. I.; Ryzhov, O. S., Free interaction of near-wall layers with the Poiseuille flow core, Dokl. Akad. Nauk SSSR, 257, 55-59, (1981)
[11] Bogdanova, E. V.; Ryzhov, O. S., On oscillations excited by a harmonic oscillator in the Poiseuille flow, Dokl. Akad. Nauk SSSR, 257, 837-841, (1981) · Zbl 0474.76051
[12] Smith, F. T., On the high Reynolds number theory of laminar flows, IMA J. Appl. Math., 28, 207-281, (1982) · Zbl 0494.76042
[13] Savenkov, I. V., Features of the linear stage of development of 3D wave packets in a plane Poiseuille flow, Comput. Math. Math. Phys., 49, 1212-1220, (2009) · Zbl 1224.76052
[14] Ryzhov, O. S.; Terent’ev, E. D., Transient regime characterizing the startup of a vibrator in a subsonic boundary layer on a plate, Prikl. Mat. Mekh., 50, 974-986, (1986)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.