Absolute Instability of Incompressible Boundary Layer over a Compliant Plate

  • I. V. Savenkov


An incompressible boundary layer on a compliant plate is considered. The influence exerted by the tensile stress and bending stiffness of the plate on the stability of the boundary layer is investigated in the limit of high Reynolds numbers on the basis of the triple-deck theory. It is shown that upstream-propagating growing waves can be generated in a certain range of parameters characterizing the plate properties. As a result, the flow becomes absolutely unstable in the conventional sense.


incompressible boundary layer Tollmien–Schlichting waves asymptotic expansions triple-deck theory compliant surface 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. O. Kramer, “Boundary-layer stabilization by distributed damping,” J. Aeronaut. Sci. 24, 458–460 (1957).Google Scholar
  2. 2.
    P. W. Carpenter and A. D. Garrad, “The hydrodynamic stability of flow over Kramer-type compliant surfaces: Part 1. Tollmien–Schlichting instabilities,” J. Fluid Mech. 155, 465–510 (1985).CrossRefMATHGoogle Scholar
  3. 3.
    P. W. Carpenter and A. D. Garrad, “The hydrodynamic stability of flow over Kramer-type compliant surfaces: Part 2. Flow-induced surface instabilities,” J. Fluid Mech. 170, 199–232 (1986).CrossRefMATHGoogle Scholar
  4. 4.
    Flow Past Highly Compliant Boundaries and in Collapsible Tubes: Proceedings of the IUTAM Symposium, University of Warwick, UK, March 26–30, 2001 (Kluwer Academic, 2003).Google Scholar
  5. 5.
    M. Gad-el-Hak, “Compliant coatings for drag reduction,” Progr. Aerospace Sci. 38 (1), 77–99 (2002).CrossRefGoogle Scholar
  6. 6.
    O. S. Ryzhov and I. V. Savenkov, “Asymptotic approach in hydrodynamic stability theory,” Mat. Model. 1 (4), 61–86 (1989).MATHGoogle Scholar
  7. 7.
    V. Ya. Neiland, “Theory of laminar boundary layer separation in supersonic flow,” Fluid Dyn. 4 (4), 33–35 (1969).CrossRefMATHGoogle Scholar
  8. 8.
    K. Stewartson and P. G. Williams, “Self-induced separation,” Proc. R. Soc. London, Ser. A 312 (1509), 181–206 (1969).CrossRefMATHGoogle Scholar
  9. 9.
    A. F. Messiter, “Boundary-layer flow near the trailing edge of a flat plate,” SIAM J. Appl. Math. 18 (1), 241–257 (1970).CrossRefMATHGoogle Scholar
  10. 10.
    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 (1), 73–79 (1995).MathSciNetMATHGoogle Scholar
  11. 11.
    I. V. Savenkov, “Effect of surface elasticity on boundary-layer stability for transonic free-stream velocities,” Comput. Math. Math. Phys. 41 (1), 130–135 (2001).MathSciNetMATHGoogle Scholar
  12. 12.
    J. D. A. Walker, A. Fletcher, and A. I. Ruban, “Instabilities of a flexible surface in supersonic flow,” Q. J. Mech. Appl. Math. 59 (2), 253–276 (2006).MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    I. V. Savenkov, “Instability of the two-dimensional Poiseuille flow between elastic plates,” Comput. Math. Math. Phys. 51 (12), 2155–2161 (2011).MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    I. V. Savenkov, “Three-dimensional instability of flow in a flat channel between elastic plates,” Comput. Math. Math. Phys. 52 (10), 1445–1451 (2012).MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    I. V. Savenkov, “Unsteady axisymmetric flow through tubes with elastic walls,” Comput. Math. Math. Phys. 36 (2), 255–267 (1996).MathSciNetMATHGoogle Scholar
  16. 16.
    O. S. Ryzhov and E. D. Terent’ev, “On the transition mode characterizing the triggering of a vibrator in the subsonic boundary layer on a plate,” J. Appl. Math. Mech. 50 (6), 753–762 (1986).CrossRefMATHGoogle Scholar
  17. 17.
    I. V. Savenkov, “Viscous instability of hypersonic flow past a wedge,” Fluid Dyn. 27 (4), 192–195 (1992).CrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,”Russian Academy of SciencesMoscowRussia

Personalised recommendations