Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-19T16:04:45.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Destabilizing effects of confinement on homogeneous mixing layers

Published online by Cambridge University Press:  06 March 2009

J. J. HEALEY
J. J. HEALEY*
Affiliation:
Department of Mathematics, Keele University, Keele, Staffs ST5 5BG, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The absolute and convective instability properties of plane mixing layers are investigated for linearized inviscid disturbances. It is shown that confinement by plates parallel to the flow can enhance the absolute instability so much that even a co-flow plane mixing layer becomes absolutely unstable when the ratio of distances of the plates from the mixing layer lies in a certain range. Even when the plates are placed equidistantly from the mixing layer, a co-flow mixing layer can become absolutely unstable if the velocity profile has an asymmetry about its mid-plane. ‘Semiconfinement’, where a plate is only added to one side of the mixing layer, is also investigated. A substantial destabilization is possible when the plate is added on the side of the faster stream. Previous investigations seem only to have found absolute instability when the streams flow in opposite directions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 623 , 25 March 2009 , pp. 241 - 271
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

Ashpis, D. E. & Reshotko, E. 1990 The vibrating ribbon problem revisited. J. Fluid Mech. 213, 531–547.Google Scholar
Briggs, R. J. 1964 Electron-Stream Interaction with Plasmas. MIT.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability Theory. CUP.Google Scholar
Gaster, M. 1968 Growth of disturbances in both space and time. Phys. Fluids 11, 723–727.Google Scholar
Healey, J. J. 2006a Inviscid long-wave theory for the absolute instability of the rotating disk-boundary layer. Proc. R. Soc. Lond. A 462, 1467–1492.Google Scholar
Healey, J. J. 2006b A new type of convective instability with exponential growth perpendicular to the basic flow. J. Fluid Mech. 560, 279–310.CrossRefGoogle Scholar
Healey, J. J. 2007 Enhancing the absolute instability of a boundary layer by adding a far away plate. J. Fluid Mech. 579, 29–61.Google Scholar
Healey, J. J. 2008 Inviscid axisymmetric absolute instability of swirling jets. J. Fluid Mech. 613, 1–33.Google Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.CrossRefGoogle Scholar
Juniper, M. P. 2006 The effect of confinement on the stability of two-dimensional shear flows. J. Fluid Mech. 565, 171–195.Google Scholar
Juniper, M. P. 2007 The full-impulse response of two-dimensional jet/wake flows and implications for confinement. J. Fluid Mech. 590, 163–185.Google Scholar
Juniper, M. P. & Candel, S. M. 2003 The stability of ducted compound flows and consequences for the geometry of coaxial injectors. J. Fluid Mech. 482, 257–269.CrossRefGoogle Scholar
Koch, W. 1985 Local instability characteristics and frequency determination of self-excited wake flows. J. Sound and Vib. 99, 53–83.Google Scholar
Lim, D. & Redekopp, L. 1998 Absolute instability conditions for variable density, swirling jet flows. Eur. J. Mech. B/Fluids 17, 165–185.Google Scholar
Michalke, A. 1964 On the inviscid instability of the hyperbolic-tangent velocity profile. J. Fluid Mech. 19, 543–556.CrossRefGoogle Scholar
Rayleigh, Lord 1894 The Theory of Sound, 2nd ed. MacMillan.Google Scholar
Yu, M.-H. & Monkewitz, P. A. 1990 The effect of nonuniform density on the absolute instability of two-dimensional inertial jets and wakes. Phys. Fluids A 2, 1175–1181.CrossRefGoogle Scholar