Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-25T05:46:18.845Z Has data issue: false hasContentIssue false
  • English
  • Français

The production of turbulent stress in a shear flow by irrotational fluctuations

Published online by Cambridge University Press:  20 April 2006

I. S. Gartshore ,
P. A. Durbin  and
J. C. R. Hunt
I. S. Gartshore
Affiliation:
The University of British Columbia, Vancouver, B.C., Canada
P. A. Durbin
Affiliation:
NASA (Lewis), Cleveland, Ohio, U.S.A.
J. C. R. Hunt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, England
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is a study of how external turbulence affects an initially turbulence-free region in which there is a mean-velocity gradient dU/dz. Rapid-distortion theory shows how external turbulence induces irrotational fluctuations in the sheared region, which interact with the shear to produce rotational velocity fluctuations and mean Reynolds stresses. These stresses extend into the sheared region over a distance of the order of the integral scale L∞. Since the actual front between the initial external turbulence and the shear flow is a randomly contorted surface, the turbulence of a fixed point near the front is intermittent. Intermittency is included in the present analysis by a simple statistical model.

Experiments were done in a wind tunnel with the flow divided by a plate extending from upstream to x = 0. Above the plate, turbulence was produced by a grid. Below the plate a low turbulence shear was produced by wire screens. The wake of the plate (x > 0) decayed downstream.

Turbulent shear stress was observed to grow from zero to significant values in the interaction region. The magnitude and extent of the observed stress agrees reasonably well with predictions. We conclude that turbulent stresses can be produced by irrotational fluctuations in a region of mean shear, and that this effect can be estimated using rapid-distortion theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 137 , December 1983 , pp. 307 - 329
Copyright
© 1983 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

Bradshaw, P. 1967 Irrotational fluctuations near a turbulent boundary J. Fluid Mech. 27, 209–230.Google Scholar
Britter, R. E., Hunt, J. C. R. & Mumford, J. C. 1979 The distortion of turbulence by a circular cylinder J. Fluid Mech. 92, 269–301.Google Scholar
Castro, I. P. 1976 Some problems concerning the production of a linear shear flow using curved wire-gauge screens J. Fluid Mech. 76, 689–709.Google Scholar
Durbin, P. A. 1978 Rapid distortion theory of turbulent flows. Ph.D thesis, University of Cambridge.
Gartshore, I. S. 1966 An experimental examination of the large-eddy equilibrium hypothesis J. Fluid Mech. 24, 89–98.Google Scholar
Goldstein, M. E. 1979 Scattering and distortion of the unsteady motion on transversely sheared mean flows J. Fluid Mech. 91, 601–632.Google Scholar
Hunt, J. C. R. 1973 A theory of turbulent flow round bluff bodies J. Fluid Mech. 61, 625–706.Google Scholar
Hunt, J. C. R. & Graham, J. M. R. 1978 Free-stream turbulence near plane boundaries J. Fluid Mech. 84, 209–235.Google Scholar
Lachmann, G. V. (ed.) 1961 Boundary Layer and Flow Control, p. 1277. Pergamon.
Maull, D. J. 1969 The wake characteristics of a bluff body in a shear flow. AGARD CP 48, Paper 16.Google Scholar
Mehta, R. D., Shabaka, I. M. M. A. & Bradshaw, P. 1981 Imbedded longitudinal vortices in turbulent boundary layers. Paper presented at Symp. on Numerical and Physical Aspects of Aerodynamic Flows, Col. State University, January 1981.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.