Skip Navigation

The Quarterly Journal of Mechanics and Applied Mathematics 1957 10(4):433-447; doi:10.1093/qjmam/10.4.433
© 1957 by Oxford University Press
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by MORTON, B. R.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

ON THE EQUILIBRIUM OF A STRATIFIED LAYER OF FLUID

B. R. MORTON

( Department of Mathematics, University College London {dagger} )

This note demonstrates the equal importance of viscosity and thermal conductivity (or any equivalent process of diffusion) in determining the departure from equilibrium of continuously stratified layers of fluid. The analysis is carried out by an extension of previous variational principles, and is applied to freely bounded horizontal layers which are thermally stratified; the initial rate of growth of small disturbances is shown to depend on the Rayleigh and Prandtl numbers. The method gives the usual critical Rayleigh number for the onset of convection in unstably stratified layers with a linear density gradient, but it also indicates that this critical value of the Rayleigh number suffers little reduction when the stratification is originally non-uniform. Although the analysis is applied to a system which cannot be realized physically, the corresponding results for real systems should be qualitatively similar.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.