Instability of the buoyancy layer on an evenly heated vertical wall
The stability of the buoyancy layer on a uniformly heated vertical wall in a stratified fluid is investigated using both semi-analytical and direct numerical methods. As in the related problem in which the excess temperature of the wall is specified, the basic laminar flow is steady and one-dimensio...
Saved in:
Published in | Journal of fluid mechanics Vol. 587; pp. 453 - 469 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Cambridge, UK
Cambridge University Press
25.09.2007
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | The stability of the buoyancy layer on a uniformly heated vertical wall in a stratified fluid is investigated using both semi-analytical and direct numerical methods. As in the related problem in which the excess temperature of the wall is specified, the basic laminar flow is steady and one-dimensional. Here flows varying in time and with height are considered, the behaviour being determined by the fluid's Prandtl number and a Reynolds number proportional to the ratio of two temperature gradients: the horizontal one imposed at the wall and the vertical one existing in the far field. For low Reynolds numbers, the flow is stable with variation only in the wall-normal direction. For Reynolds numbers greater than a critical value, depending on the Prandtl number, the flow is unstableand supports two-dimensional travelling waves. The critical Reynolds number and other properties have been obtained via linearized stability analysis and are shown to accuratelypredict the behaviour of the full nonlinear solution obtained numerically for Prandtl number 7. The stability analysis employs a novel Laguerre collocation scheme while the direct numerical simulations use a second-order finite volume method. |
---|---|
Bibliography: | ark:/67375/6GQ-2KKGD7FM-8 PII:S0022112007007318 istex:4E4A8035AD1226E6BE66EC40BB6541D2D7D293FE ArticleID:00731 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0022-1120 1469-7645 |
DOI: | 10.1017/S0022112007007318 |