Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-10T06:05:33.687Z Has data issue: false hasContentIssue false
  • English
  • Français

On the spatial instability of piecewise linear free shear layers

Published online by Cambridge University Press:  21 April 2006

T. F. Balsa
T. F. Balsa
Affiliation:
Aerospace and Mechanical Engineering Department, University of Arizona, Tucson, AZ 85721, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The main goal of this paper is to clarify the spatial instability of a piecewise linear free shear flow. We do this by obtaining numerical solutions to the Orr–Sommerfeld equation at high Reynolds numbers. The velocity profile chosen is very much like a piecewise linear one, with the exception that the corners have been rounded so that the entire profile is infinitely differentiable. We find that the (viscous) spatial instability of this modified profile is virtually identical to the inviscid spatial instability of the piecewise linear profile and agrees qualitatively with the inviscid results for the tanh profile when the shear layers are convectively unstable. The unphysical features, previously identified for the piecewise linear velocity profile, arise only when the flow is absolutely unstable. In a nutshell, we see nothing wrong with the inviscid spatial instability of piecewise linear shear flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 174 , January 1987 , pp. 553 - 563
Copyright
© 1987 Cambridge University Press

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

Balsa, T. F. 1986 On the receptivity of free shear layers (to be published).
Bechert, D. 1972 Über mehrfache und stromauf laufende Wellen in Freistrahlen. DFVLR Rep. DLR-FB 72–06.
Drazin, P. G. & Reid, W. H. 1982 Hydrodynamic Stability. Cambridge University Press.
Esch, R. E. 1957 The instability of a shear layer between two parallel steams. J. Fluid Mech. 3, 289–303.Google Scholar
Huerre, P. & Monkewitz, P. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.Google Scholar
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521–544.Google Scholar
Rayleigh, Lord 1945 The Theory of Sound, vol. 2. Dover.