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Turbulence statistics in Couette flow at high Reynolds number

Published online by Cambridge University Press:  08 October 2014

Sergio Pirozzoli ,
Matteo Bernardini  and
Paolo Orlandi
Sergio Pirozzoli*
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Rome, Italy
Matteo Bernardini
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Rome, Italy
Paolo Orlandi
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Rome, Italy
*
†Email address for correspondence: sergio.pirozzoli@uniroma1.it
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Abstract

We investigate the behaviour of the canonical turbulent Couette flow at computationally high Reynolds number through a series of large-scale direct numerical simulations. We achieve a Reynolds number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}_{\tau } = h/\delta _v \approx 1000$, where $h$ is the channel half-height and $\delta _v$ is the viscous length scale at which some phenomena representative of the asymptotic Reynolds-number regime manifest themselves. While a logarithmic mean velocity profile is found to provide a reasonable fit of the data, including the skin friction, closer scrutiny shows that deviations from the log law are systematic, and probably increasing at higher Reynolds numbers. The Reynolds stress distribution shows the formation of a secondary outer peak in the streamwise velocity variance, which is associated with significant excess of turbulent production as compared to the local dissipation. This excess is related to the formation of large-scale streaks and rollers, which are responsible for a substantial fraction of the turbulent shear stress in the channel core, and for significant increase of the turbulence intermittency in the near-wall region.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 758 , 10 November 2014 , pp. 327 - 343
Copyright
© 2014 Cambridge University Press 

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