Hostname: page-component-7c8c6479df-ws8qp Total loading time: 0 Render date: 2024-03-28T06:01:26.149Z Has data issue: false hasContentIssue false

Equilibrium and relaxation in turbulent wakes

Published online by Cambridge University Press:  29 March 2006

R. Narasimha
Affiliation:
Department of Aeronautical Engineering, Indian Institute of Science, Bangalore Present address: Department of Mathematics, University of Strathclyde, Glasgow.
A. Prabhu
Affiliation:
Department of Aeronautical Engineering, Indian Institute of Science, Bangalore

Abstract

In order to study the memory of the larger eddies in turbulent shear flow, experiments have been conducted on plane turbulent wakes undergoing transition from an initial (carefully prepared) equilibrium state to a different final one, as a result of a nearly impulsive pressure gradient. It is shown that under the conditions of the experiments the equations of motion possess self-preserving solutions in the sense of Townsend (1956), but the observed behaviour of the wake is appreciably different when the pressure gradient is not very small, as the flow goes through a slow relaxation process before reaching final equilibrium. Measurements of the Reynolds stresse show that the approach to a new equilibrium state is exponential, with a relaxation length of the order of 103 momentum thicknesses. It is suggested that a flow satisfying the conditions required by a self-preservation analysis will exhibit equilibrium only if the relaxation length is small compared with a characteristic streamwise length scale of the flow.

Type
Research Article
Copyright
© 1972 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

Batchelor, G. K. & Proudman, I. 1954 Quart. J. Mech. Appl. Math. 7, 83.
Bradshaw, P. 1966 J. Fluid Mech. 25, 225.
Bradshaw, P., Ferriss, D. H. & Atwell, N. P. 1967 J. Fluid Mech. 28, 593.
Clauser, F. 1954 J. Aero. Sci. 21, 91.
Clauser, F. 1956 Adv. Appl. Mech. 4, 1.
Coles, D. 1956 J. Fluid Mech. 1, 191.
Coles, D. 1969 In: Kline et al. (1969).
Gartshore, I. S. 1967 J. Fluid Mech. 30, 547.
Hill, P. G. 1962 M.I.T. Gas Turbine Lab. Rep. no. 65.
Kline, S. J., Morkovin, M. V., Sovran, G. & Cockrell, D. J. (eds) 1969 Computation of Turbulent Boundary Layers. Proc. AFOSR-IFP-Stanford Conference. Thermosciences Division, Department of Mechanical Engineering, Stanford.
Narasimha, R. & Prabhu, A. 1971 I.I.Sc. Aero Rep. 71FM3.
Prabhu, A. 1966 A.I.A.A. J. 4, 925.
Prabhu, A. 1968 I.I.Sc. Aero Rep. AE 228 A.
Prabhu, A. & Narasimha, R. 1972 J. Fluid Mech. 54, 1.
Ramjee, V., Badri Narayanan, M. A. & Narasimha, R. 1972 Z. angew. Math. Phys. to appear.
Schlichting, H. 1955 Boundary Layer Theory. Pergamon Press.
Tani, I. 1969 In: Kline et al. (1969).
Townsend, A. A. 1949 Aust. J. Sci. Res. 2, 451.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Uberoi, M. S. & Freymuth, P. 1969 Phys. Fluids, 12, 1359.