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The stability of a two-dimensional laminar jet

Published online by Cambridge University Press:  28 March 2006

T. Tatsumi  and
T. Kakutani
T. Tatsumi
Affiliation:
Cavendish Laboratory, University of Cambridge
Now on leave from University of Kyoto, Japan.
T. Kakutani
Affiliation:
Department of Physics, University of Kyoto
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Abstract

This paper deals with the stability of a two-dimensional laminar jet against the infinitesimal antisymmetric disturbance. The curve of the neutral stability in the (α, R)-plane (α, the wave-number; R, Reynolds number) is calculated using two different methods for the different parts of the curve; the solution is developed in powers of (αR)−1 for obtaining the upper branch of the curve and in powers of αR for the lower branch.

The asymptotic behaviour of these branches is that for branch I,$\alpha \rightarrow 2, \;\; c \rightarrow \frac{2}{3}$ for $R \rightarrow \infty$; and for branch II, $R \sim 1\cdot12\alpha^{-1|2},\; c \sim 1\cdot 20 \alpha^2$ for α → 0. Some discussion is given on the validity of the basic assumption of the stability theory in relation to the numerical result obtained here.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 4 , Issue 3 , July 1958 , pp. 261 - 275
Copyright
© Cambridge University Press

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