Generalized Coles' law and outer layer conformal mapping

Abstract

The time-averaged velocity profile of a turbulent boundary layer can be predicted by combining its different trends in the inner and outer regions in a single law of the wake. A new non-dimensional coordinate system that projects the time-averaged velocity profiles of the inner and the outer regions on the same non-dimensional plane is introduced, leading to a unified treatment for the mixing region. In this coordinate system, various laws of the wake are shown to be the same but a constant. The non-dimensionalization is tested on a specific law of the wake, in which the closure coefficients are regressed from wind tunnel measurements and direct numerical simulations of turbulent boundary layers under zero-pressure gradient, over a good range of boundary layer thickness based Reynolds numbers. This data fit produced profiles within 2% of the reference values. This is of practical use to numerical modellers for generating boundary layer inflow profiles.

Keywords:

• Boundary layer model
• law of the wake
• scaling law
• turbulent boundary layer
• wake parameter

Acknowledgement

This research project was supported by a Marie Curie Early Stage Research Training Fellowship of the European Community's Sixth Framework Programme under contract number MEST CT 2005 020301.