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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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