Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-12T21:37:00.349Z Has data issue: false hasContentIssue false
  • English
  • Français

An asymptotic solution for slightly buoyant laminar plumes

Published online by Cambridge University Press:  29 March 2006

P. Wesseling
P. Wesseling
Affiliation:
Department of Applied Mathematics, Twente University of Technology, Ensehede, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

When the buoyancy forces are small compared with the inertia forces, heated plumes in laminar flows which are uniform at upstream infinity approximately satisfy a linearized version of the Boussinesq equations, here called the Oseen–Boussinesq equations. An analytic solution is constructed for arbitrary Prandtl number and arbitrary direction of the unperturbed flow in the case of a plume produced by a point source. The two-dimensional case of the plume from a line source is considered briefly. A Stokes-type paradox occurs: it is found that a line-source solution that vanishes at infinity does not exist.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 70 , Issue 1 , 15 July 1975 , pp. 81 - 87
Copyright
© 1975 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

Csanady, C. T. 1965 The buoyant motion within a hot gas plume in a horizontal wind. J. Fluid Mech. 22, 225.Google Scholar
Lamb, H. 1911 On the uniform motion of a sphere through a viscous fluid. Phil. Mag. 21, 112.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn, p. 610. Cambridge University Press.
Miles, J. W. 1969 Waves and wave drag in stratified flows. Proc. 12th Int. Cong. Appl. Mech., p. 50. Springer.
Ostrach, S. 1964 Laminar flows with body forces. In Theory of Laminar Flows (ed. F. K. Moore), p. 528. Princeton University Press.
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.
Watson, G. N. 1958 A Treatise on the Theory of Bessel Functions, 2nd edn. Cambridge University Press.