Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-26T22:26:54.688Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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

Bickley, W. 1937 Phil. Mag. 23, 727.
Curle, N. 1957 Proc. Roy. Soc. A, 238, 489.
Foote, J. R. & Lin, C. C. 1950 Quart. Appl. Math. 8, 265.
Lessen, M. 1950 Nat. Adv. Comm. Aero., Wash., Rep. no. 979.
Lin, C. C. 1955 The Theory of Hydrodynamical Stability. Cambridge University Press.
McKoen, C. H. 1957 Aero. Res. Counc., Lond., Curr. Pap. no. 303.
Pai, S. I. 1951 J. Aero. Sci. 18, 731.
Savic, P. 1941 Phil. Mag. 32, 245.
Schlichting, H. 1933 Z. Angew. Math. Mech. 13, 260.
Squire, H. B. 1933 Proc. Roy. Soc. A, 142, 621.