Steady boundary-layer solutions for a swirling stratified fluid in a rotating cone

Hewitt, R.E. and Duck, P.W. and Foster, M.R. (1999) Steady boundary-layer solutions for a swirling stratified fluid in a rotating cone. Journal of Fluid Mechanics, 384. pp. 339-374. ISSN 1469-7645

PDF HewittDuckFoster99_JFM.pdf Download (2MB)

Abstract

We consider a set of nonlinear boundary-layer equations that have been derived by Duck, Foster & Hewitt (1997a, DFH), for the swirling flow of a linearly stratified fluid in a conical container. In contrast to the unsteady analysis of DFH, we re- strict attention to steady solutions and extend the previous discussion further by allowing the container to both co-rotate and counter-rotate relative to the contained swirling fluid. The system is governed by three parameters, which are essentially non- dimensional measures of the rotation, stratification and a Schmidt number. Some of the properties of this system are related (in some cases rather subtly) to those found in the swirling flow of a homogeneous fluid above an infinite rotating disk; however, the introduction of buoyancy effects with a sloping boundary leads to other (new) behaviours. A general description of the steady solutions to this system proves to be rather complicated and shows many interesting features, including non-uniqueness, singular solutions and bifurcation phenomena. We present a broad description of the steady states with particular emphasis on boundaries in parameter space beyond which steady states cannot be continued. A natural extension of this work (motivated by recent experimental results) is to investigate the possibility of solution branches corresponding to non-axisymmetric boundary-layer states appearing as bifurcations of the axisymmetric solutions. In an Appendix we give details of an exact, non-axisymmetric solution to the Navier� Stokes equations (with axisymmetric boundary conditions) corresponding to the flow of homogeneous fluid above a rotating disk.

Item Type:	Article
Additional Information:	© 1999 Cambridge University Press
Uncontrolled Keywords:	Ekman boundary layer rotating flow slope
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 47 Fluid dynamics
Depositing User:	Dr Richard E. Hewitt
Date Deposited:	14 Nov 2013
Last Modified:	20 Oct 2017 14:13
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2052

Actions (login required)

View Item