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A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis

Published online by Cambridge University Press:  26 April 2006

A. E. Perry  and
Ivan Marušić
A. E. Perry
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Melbourne, Parkville, Victoria 3052, Australia
Ivan Marušić
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Melbourne, Parkville, Victoria 3052, Australia
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Abstract

The attached eddy hypothesis developed for zero pressure gradient boundary layers and for pipe flow is extended here to boundary layers with arbitrary streamwise pressure gradients, both favourable and adverse. It is found that in order to obtain the correct quantitative results for all components of the Reynolds stresses, two basic types of eddy structure geometries are required. The first type, called type-A, is interpreted to give a ‘wall structure’ and the second, referred to as type-B, gives a ‘wake structure’. This is in analogy with the conventional mean velocity formulation of Coles where the velocity is decomposed into a law of the wall and a law of the wake.

If the above mean velocity formulation is accepted, then in principle, once the eddy geometries are fixed for the two eddy types, all Reynolds stresses and associated spectra contributed from the attached eddies can be computed without any further empirical constants. This is done by using the momentum equation and certain convolution integrals developed here based on the attached eddy hypothesis. The theory is developed using data from equilibrium and quasi-equilibrium flows. In Part 2 the authors’ non-equilibrium data are used.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 298 , 10 September 1995 , pp. 361 - 388
Copyright
© 1995 Cambridge University Press

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References

Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aero. Sci. 21, 91–108.Google Scholar
Clauser, F. H. 1956 The turbulent boundary layer. Adv. Appl. Mech. 4, 1–51.Google Scholar
Coles, D. E. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.Google Scholar
Coles, D. E. 1957 Remarks on the equilibrium turbulent boundary layer. J. Aero. Sci. 24, 459–506.Google Scholar
East, L. F., Sawyer, W. G. & Nash, C. R. 1979 An investigation of the structure of equilibrium turbulent boundary layers. RAE Tech. Rep. 79040.
Lewkowicz, A. K. 1982 An improved universal wake function for turbulent boundary layers and some of its consequences. Z. Flugwiss. Weltraumforsch. 6, 261–266.Google Scholar
Marušić, I. 1991 The structure of zero- and adverse- pressure gradient turbulent boundary layers. PhD thesis, University of Melbourne.
Marušić, I. & Perry, A. E. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support. J. Fluid Mech. 298, 389–407.Google Scholar
Perry, A. E. 1968 A theoretical study of equilibrium turbulent boundary layers. Originally unpublised; now, Rep. FM-19, 1992 Dept. of Mech. Engng, University of Melbourne.
Perry, A. E. 1992 A new look at some closure problems of turbulent boundary layers. GALCIT Rep. FM-92-4. California Institute of Technology.
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217.Google Scholar
Perry, A. E., Henbest, S. M. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.Google Scholar
Perry, A. E. & Li, J. D. 1990 Experimental support for the attached eddy hypothesis in zeropressure-gradient turbulent boundary layers. J. Fluid Mech. 218, 405–438.Google Scholar
Perry, A. E. & Li, J. D. 1991 Theoretical and experimental studies of shear stress profiles in two dimensional turbulent boundary layers. Rep. FM-18. Dept. of Mech. Engng, University of Melbourne.
Perry, A. E., Li, J. D. & Marušić, I. 1991 Towards a closure scheme for turbulent boundary layers using the attached eddy hypothesis. Phil Trans. R. Soc. Lond. A 336, 67–79.Google Scholar
Perry, A. E., Lim, K. L. & Henbest, S. M. 1987 An experimental study of the turbulence structure in smooth- and rough-wall boundary layers. J. Fluid Mech. 177, 437–466.Google Scholar
Perry, A. E., Marušić, I. & Li, J. D. 1993 A wall-wake model for the turbulence structure of boundary layers using attached eddies. Rep. FM-21. Dept. of Mech. Engng, University of Melbourne.
Perry, A. E., Marušić, I. & Li, J. D. 1994 Wall turbulence closure based on classical similarity laws and the attached eddy hypothesis. Phys. Fluids 6, 1024–1035.Google Scholar
Rotta, J. C. 1962 Turbulent boundary layers in incompressible flow. Prog. Aero. Sci. 2, 1–219.Google Scholar
Skåre, P. E. & Krogstad, P.-A. 1994 A turbulent boundary layer near separation. J. Fluid Mech. 272, 319–348.Google Scholar
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97–120.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Winckelmans, G. S. & Leonard, A. 1993 Contributions to vortex particle methods for the computation of three-dimensional incompressible unsteady flows. J. Comput. Phys. 109, 247–273.Google Scholar