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Scaling of the turbulent/non-turbulent interface in boundary layers

Published online by Cambridge University Press:  19 June 2014

Kapil Chauhan ,
Jimmy Philip  and
Ivan Marusic
Kapil Chauhan*
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Parkville, VIC 3010, Australia
Jimmy Philip
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Parkville, VIC 3010, Australia
Ivan Marusic
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Parkville, VIC 3010, Australia
*
†Email address for correspondence: kchauhan@unimelb.edu.au
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Abstract

Scaling of the interface that demarcates a turbulent boundary layer from the non-turbulent free stream is sought using theoretical reasoning and experimental evidence in a zero-pressure-gradient boundary layer. The data-analysis, utilising particle image velocimetry (PIV) measurements at four different Reynolds numbers ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\delta u_{\tau }/\nu =1200\mbox{--}14\, 500$), indicates the presence of a viscosity dominated interface at all Reynolds numbers. It is found that the mean normal velocity across the interface and the tangential velocity jump scale with the skin-friction velocity $u_{\tau }$ and are approximately $u_{\tau }/10$ and $u_{\tau }$, respectively. The width of the superlayer is characterised by the local vorticity thickness $\delta _{\omega }$ and scales with the viscous length scale $\nu /u_{\tau }$. An order of magnitude analysis of the tangential momentum balance within the superlayer suggests that the turbulent motions also scale with inner velocity and length scales $u_{\tau }$ and $\nu /u_{\tau }$, respectively. The influence of the wall on the dynamics in the superlayer is considered via Townsend’s similarity hypothesis, which can be extended to account for the viscous influence at the turbulent/non-turbulent interface. Similar to a turbulent far-wake the turbulent motions in the superlayer are of the same order as the mean velocity deficit, which lends to a physical explanation for the emergence of the wake profile in the outer part of the boundary layer.

JFM classification

Boundary Layers: Boundary Layers Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 751 , 25 July 2014 , pp. 298 - 328
Copyright
© 2014 Cambridge University Press 

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