Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T09:03:43.852Z Has data issue: false hasContentIssue false
  • English
  • Français

On the non-existence of subcritical instabilities in fluid layers heated from below

Published online by Cambridge University Press:  28 March 2006

R. Sani
R. Sani
Affiliation:
Department of Mathematics, Rensselaer Polytechnic Institute, Troy, New York Present address: Department of Chemical Engineering, University of Illinois, Urbana, Illinois.
Get access Rights & Permissions [Opens in a new window]

Abstract

Using some recent results it is established that, for very general boundary conditions, time-independent subcritical instabilities do not exist for the non-linear thermoconvective stability problem.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 20 , Issue 2 , October 1964 , pp. 315 - 319
Copyright
© 1964 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

Ladyzhenskaya, O. A. 1963 The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach.
Phillips, H. B. 1933 Vector Analysis. New York: John Wiley.
Sani, R. L. & Scriven, L. E. 1964 Convective instability. I. To be submitted to Phys. Fluids.Google Scholar
Stuart, J. T. 1960 Non-linear effects in hydrodynamic stability. Proc. X-th Int. Congr. Appl. Math. pp. 63–97. Stresa, Elsevier.
Stuart, J. T. 1960 On the nonlinear mechanics of wave disturbances in stable and unstable parallel flow, I. J. Fluid Mech. 9, 353–70.Google Scholar
Ukhovskii, M. R. & Iudovich, V. I. 1963 On the equations of steady-state convection. Prik. Math. Mek. 27, 432–40.Google Scholar
Watson, J. 1960 On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows, II. J. Fluid Mech. 9, 371–89.Google Scholar