Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-29T01:04:42.532Z Has data issue: false hasContentIssue false
  • English
  • Français

Feedback Instability in a Boundary-Layer Flow Over Roughness

Part of: Hydrodynamic stability

Published online by Cambridge University Press:  21 December 2009

S. N. Timoshin
S. N. Timoshin
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT
Get access

Abstract

Linear stability of an incompressible triple-deck flow over a wall roughness is considered for disturbances of high frequency. The wall roughness consists of two relatively short obstacles placed far apart on an otherwise flat surface. It is shown that the flow is unstable to feedback or global mode disturbances. The feedback loop is formed by algebraically decaying disturbances propagating upstream and weakly growing Tollmien-Schlichting waves travelling downstream and as such represents an interaction between modes from continuous and discrete spectra of the corresponding parallel-flow problem. An example of growth rate calculation for a specific roughness is considered.

MSC classification

Secondary: 76E09: Stability and instability of nonparallel flows
Type
Research Article
Information
Mathematika , Volume 52 , Issue 1-2 , December 2005 , pp. 161 - 168
Copyright
Copyright © University College London 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Chomaz, J.-M., Huerre, P. and Redekopp, L. G.. A frequency selection criterion in spatially developing flows. Stud. Appl. Math. 84 (1991), 119–144.CrossRefGoogle Scholar
2Huerre, P. and Monkewitz, P. A.. Local and global instabilities in spatially developing flows. Ann. Rev. Fluid Mech. 22 (1990), 473–537.CrossRefGoogle Scholar
3Rothmayer, A. P. and Smith, F. T.. Incompressible triple-deck theory. In The Handbook of Fluid Dynamics, ed. Johnson, R., Springer (1998).Google Scholar
4Ryzhov, O. S. and Terent'ev, E. D.. On the transition regime characterising the start of a vibrator in a subsonic boundary layer on a plate. Prikl. Matem. Mekh. 50(6) (1986), 974–986.Google Scholar
5Smith, F. T.. On the non-parallel flow stability of the Blasius boundary layer. Proc. Roy. Soc. Lond. 366 (1979), 91–109.Google Scholar
6Smith, F. T. and Bodonyi, R. J.. On short-scale inviscid instabilities in flow past surface-mounted obstacles and other non-parallel motions. Aero. J. June/July (1985), 205–212.CrossRefGoogle Scholar
7Stewartson, K.. Multi-structured boundary layers on flat plates and related bodies. Adv. Appl. Mech. 14 (1974), 145–239.CrossRefGoogle Scholar
8Sychev, V. V., Ruban, A. I., ic. Sychev, V. and Korolev, G. L.. Asymptotic Theory of Separated Flows. Cambridge University Press (1998).CrossRefGoogle Scholar
9Timoshin, S. N. and Smith, F. T.. Non-local interactions and feedback instability in a high Reynolds number flow. Theoret. Comp. Fluid Dyn., submitted (2000).Google Scholar
10Tutty, O. R. and Cowley, S. J.. On the stability and the numerical solution of the unsteady interactive boundary-layer equation. J. Fluid Mech. 168 (1986), 431–456.CrossRefGoogle Scholar
11Zhuk, V. I. and Ryzhov, O. S.. Free interaction and stability of an incompressible boundary layer. Dokl. Akad. Nauk USSR 263 (1980), 56–59 (in Russian).Google Scholar