Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-18T21:51:26.709Z Has data issue: false hasContentIssue false
  • English
  • Français

Degenerate bifurcation in stably stratified plane Poiseuille flow

Published online by Cambridge University Press:  21 May 2009

K. FUJIMURA  and
R. E. KELLY
K. FUJIMURA
Affiliation:
Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki 319-11, Japan
R. E. KELLY
Affiliation:
Mechanical and Aerospace Engineering Department, University of California, Los Angeles, CA 90095-1597, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Bifurcation characteristics of stably stratified plane Poiseuille flow have been investigated on a weakly nonlinear basis. It is found that the results are sensitive to the value of the Prandtl number, in that subcritical bifurcation persists for most values of the Prandtl number but is replaced by supercritical bifurcation over a range of small values of the Prandtl number. This range includes values characteristic of some liquid metals. The bifurcation becomes degenerate at a particular parameter set where the real part of the cubic nonlinear coefficient in the Stuart–Landau equation vanishes at criticality, and the situation is discussed by including higher-order terms in the manner of Eckhaus & Iooss (1989). An exact hyper-degenerate situation is also found to be possible for which the cubic and the quintic nonlinear coefficients lose their real parts simultaneously; this case is also analysed. For large values of the Prandtl number, stable stratification tends to promote subcritical instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 331 , 25 January 1997 , pp. 261 - 282
Copyright
© 1997 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.)