Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T01:31:54.221Z Has data issue: false hasContentIssue false
  • English
  • Français

A nonexistence result for axially symmetric flows with constant angular velocities at infinity

Published online by Cambridge University Press:  14 November 2011

Alan R. Elcrat  and
David Siegel
Alan R. Elcrat
Affiliation:
Wichita State University
David Siegel
Affiliation:
New Mexico Institute of Mining and Technology
Get access Rights & Permissions [Opens in a new window]

Synopsis

If von Kármán's substitution is made in the Navier-Stokes equations, and boundary conditions corresponding to a flow in all of space with constant angular velocities at infinity are imposed, a boundary value problem analgous to those for flow above a rotating disk and between rotating disks is obtained. It is shown here that this problem has no solution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 3-4 , 1983 , pp. 229 - 231
Copyright
Copyright © Royal Society of Edinburgh 1983

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

1von Kármán, T.. Über laminare und turbulente Reibung. Z. Angew.Math. Mech. 1 (1921), 233–252.CrossRefGoogle Scholar
2Batchelor, G. K.. Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow. Quart. J. Mech. Appl. Math. 4 (1951), 29–41.CrossRefGoogle Scholar
3McLeod, J. B.. The existence of axially symmetric flow above a rotating disk. Proc. Roy. Soc. London Ser. A 324 (1971), 391–414.Google Scholar
4Hartman, P.. The swirling flow in boundary layer theory. Arch. Rational Mech. Anal. 42 (1971), 137–156.CrossRefGoogle Scholar