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On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients

Published online by Cambridge University Press:  11 July 2002

A. E. PERRY
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Melbourne, Parkville, Victoria 3052, Australia
IVAN MARUSIC
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455 USA
M. B. JONES
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Melbourne, Parkville, Victoria 3052, Australia

Abstract

A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such as the log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of Perry & Marusic (1995) can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.

Type
Research Article
Copyright
© 2002 Cambridge University Press

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