Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-20T16:50:06.462Z Has data issue: false hasContentIssue false
  • English
  • Français

Evolution of the flow field associated with a streamwise diffusing vortex

Published online by Cambridge University Press:  20 April 2006

C. Frederick Pearson  and
F. H. Abernathy
C. Frederick Pearson
Affiliation:
Harvard University, Division of Applied Sciences, Cambridge, Massachusetts 02138
F. H. Abernathy
Affiliation:
Harvard University, Division of Applied Sciences, Cambridge, Massachusetts 02138
Get access Rights & Permissions [Opens in a new window]

Abstract

The evolution of a shear flow with an imbedded streamwise vortex is considered. An idealized model for the vortical structure is used; the vortex is assumed to be of infinite extent in the stream direction, and to be a potential vortex (vortex filament) turned on at time zero, and subsequently allowed to diffuse under the action of viscosity. The ambient flow is taken to be, initially, a linear shear profile; the flow then evolves under the joint action of viscosity and convection induced by the vortex. Boundaries are assumed to be infinitely removed from the vortex core. A similarity variable is found which reduces the equation for the induced streamwise velocity perturbation to an ordinary differential equation, which is easily solved numerically. The vortex Reynolds number, circulation/viscosity, is found to be of prime importance. Calculated velocity profiles are presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 146 , September 1984 , pp. 271 - 283
Copyright
© 1984 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

Benney, D. J. 1961 A non-linear theory for oscillations in a parallel flow. J. Fluid Mech. 10, 209–236.Google Scholar
Blackwelder, R. F. & Eckelmann, H. 1979 Streamwise vortices associated with the bursting phenomenon. J. Fluid Mech. 94, 577–594.Google Scholar
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50, 133–160.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12, 1–34.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.Google Scholar
Taylor, G. I. 1918 On the dissipation of eddies. Reports & Memoranda of the Advisory Committee for Aeronautics, no. 598. In The Scientific Papers of Sir G. I. Taylor, vol. II (ed. G. K. Batchelor), Cambridge University Press, 1960.
Willmarth, W. W. 1975 Structure of turbulence in boundary layers. Adv. Appl. Mech. 15, 159–254.Google Scholar