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Whittaker, Robert J. 
ORCID: https://orcid.org/0000-0001-9598-5938 and Lister, John R.
(2006)
Steady axisymmetric creeping plumes above a planar boundary. Part 1. A point source.
Journal of Fluid Mechanics, 567.
pp. 361-378.
ISSN 0022-1120
Abstract
Asymptotic solutions are obtained for the rise of an axisymmetric hot plume from a localized source at the base of a half-space filled with very viscous fluid. We consider an effectively point source, generating a prescribed buoyancy flux $B$, and show that the length scale of the plume base is $z_0 \,{=}\, (32\upi \kappa^2\nu/B)$, where $\nu$ and $\kappa$ are the kinematic viscosity and thermal diffusivity. The internal structure of the plume for $z \,{\gg}\, z_0$ is found using stretched coordinates, and this is matched to a slender-body expansion for the external Stokes flow. Solutions are presented for both rigid (no-slip) and free-slip (no tangential stress) conditions on the lower boundary. In both cases we find that the typical vertical velocity in the plume increases slowly with height as $(B/\nu)^{1/2} [\ln (z/z_0)]^{1/2}$, and the plume radius increases as $(zz_0)^{1/2} [\ln (z/z_0)]^{-1/4}$.
| Item Type: | Article |
|---|---|
| Faculty \ School: | Faculty of Science > School of Mathematics |
| UEA Research Groups: | Faculty of Science > Research Groups > Fluid and Solid Mechanics |
| Depositing User: | Robert Whittaker |
| Date Deposited: | 10 Mar 2011 12:48 |
| Last Modified: | 13 Feb 2023 12:30 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/20893 |
| DOI: | 10.1017/S0022112006002370 |
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