A linear stability analysis is performed for two‐ and three‐dimensional steady source and sink flows. Cases studied include inviscid compressible and incompressible fluids. For two‐dimensional flows viscous incompressible fluid is also examined. The one‐dimensional nature of the unperturbed base flow suggested taking the vorticity as a perturbation in order to reduce the number of variables and to simplify the analysis. It is shown that source flows are always unstable. Sink flows are found unstable for inviscid compressible fluid and also for two‐dimensional flow of viscous incompressible fluid for low Reynolds numbers. The different modes of instability existing in perturbed flow are obtained.
REFERENCES
1.
M.
Goldshtik
, F.
Hussain
, and V.
Shtern
, “Symmetry breaking in vortex-source and Jeffery-Hamel flows
,” J. Fluid Mech.
232
, 521
(1991
).2.
P. M.
Eagles
, “The stability of a family of Jeffery-Hamel solutions of divergent channel flow
,” J. Fluid Mech.
24
, 191
(1966
).3.
M.
Shapira
, D.
Degani
, and D.
Weihs
, “Viscous flow in a divergent channel of arbitrary angle and its stability
,” PhysicoChem. Hydrodyn.
9
, 501
(1987
).4.
S.
Friedlander
and M.
Vishik
, “Instability criteria for the flow of an inviscid incompressible fluid
,” Phys. Rev. Lett.
66
, 2204
(1991
).5.
S.
Friedlander
and M.
Vishik
, “Instability criteria for steady flows of a perfect fluid
,” Chaos
2
, 455
(1992
).6.
H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge 1932).
7.
L. M. Milne-Thomson, Theoretical Hydrodynamics (Macmillan, London, 1968).
8.
A. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow (Ronald Press, New York, 1953), Vols. I and II.
9.
M.
Shusser
and D.
Weihs
, “Two-dimensional viscous compressible sink flows
,” Fluid Dyn. Res.
15
, 349
(1995
).10.
G. Korn and T. Korn, Mathematical Handbook (McGraw-Hill, New York, 1968).
11.
A. Erdelyi, Higher Transcendental Functions (McGraw-Hill, New. York, 1953), Vol. II.
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© 1995 American Institute of Physics.
1995
American Institute of Physics
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