Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-18T22:08:39.779Z Has data issue: false hasContentIssue false
  • English
  • Français

The base-flow and near-wake problem at very low Reynolds numbers - Part 1. The Stokes approximation

Published online by Cambridge University Press:  28 March 2006

H. Viviand  and
S.A. Berger
H. Viviand
Affiliation:
University of California, Berkeley
S.A. Berger
Affiliation:
University of California, Berkeley
Get access Rights & Permissions [Opens in a new window]

Abstract

The general solutions of the Stokes approximate equations of motion are derived for two-dimensional and axisymmetric flows in the half-space x > 0, for an arbitrarily given velocity field in the plane x = 0. There is assumed to be no solid surface in the half-space. According to whether the velocity at infinity is zero or not, the solutions can be said to describe either jet-type or wake-type flows. Only the latter category is considered; numerical examples are worked out and properties of the base flow at very low Reynolds numbers are investigated. A recirculating flow region may exist, but the flow properties are not sensitive to this feature.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 23 , Issue 3 , November 1965 , pp. 417 - 438
Copyright
© 1965 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

Almansi, E. 1899 Sull ‘integrazione dell’ equazione differenziale= 0. Ann. Mat. Pura Appl. 2, 1.Google Scholar
Brousse, P. 1956 Résolution de divers problèmes du type Stokes-Beltrami posés par la Technique Aéronautique. Publ. Sci. Tech. Minist. Air no. 323.Google Scholar
Courant, R. & Hilbert, D. 1962 Methods of Mathematical Physics, vol. II. New York: Interscience.
Dean, W. R. 1936 Note on the slow motion of fluid. Phil. Mag. 21, 727.Google Scholar
Finn, R. & Noll, W. 1957 On the uniqueness and non-existence of Stokes flows. Arch. Rat. Mech. Anal. 1, 97.Google Scholar
Förste, J. 1963 Die ebene laminare strömung in einem halbraum bei kleiner Reynolds- Zahl. Z. Angew. Math. Mech. 43, 353.Google Scholar
Kavanau, L. L. 1956 Base pressure studies in rarefied supersonic flows. J. Aero. Sci. 23, 193.Google Scholar
Payne, L. E. 1958 Representation formulas for solutions of a class of partial differential equations. Univ. of Maryland, Inst. for Fluid Dynamics and Appl. Math. Tech. Note no. BN-122.
Payne, L. E. & Pell, W. H. 1960 The Stokes flow problem for a class of axially symmetric bodies. J. Fluid Mech. 7, 529.Google Scholar
Weinstein, A. 1955 On a class of partial differential equations of even order. Ann. Mat. Pura Appl. 39, 245.Google Scholar