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Restricted nonlinear model for high- and low-drag events in plane channel flow

Published online by Cambridge University Press:  04 February 2019

Frédéric Alizard Open the ORCID record for Frédéric Alizard [Opens in a new window]  and
Damien Biau Open the ORCID record for Damien Biau [Opens in a new window]
Frédéric Alizard*
Affiliation:
LMFA, CNRS, Ecole Centrale de Lyon, Université Lyon 1, INSA Lyon, 43 Boulevard du 11 Novembre 1918, 69100 Villeurbanne, France
Damien Biau
Affiliation:
DynFluid Laboratory, Arts et Métiers ParisTech, 151 Boulevard de l’Hôpital, 75013 Paris, France
*
†Email address for correspondence: frederic.alizard@univ-lyon1.fr
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Abstract

A restricted nonlinear (RNL) model, obtained by partitioning the state variables into streamwise-averaged quantities and superimposed perturbations, is used in order to track the exact coherent state in plane channel flow investigated by Toh & Itano (J. Fluid Mech., vol. 481, 2003, pp. 67–76). When restricting nonlinearities to quadratic interaction of the fluctuating part into the streamwise-averaged component, it is shown that the coherent structure and its dynamics closely match results from direct numerical simulation (DNS), even if only a single streamwise Fourier mode is retained. In particular, both solutions exhibit long quiescent phases, spanwise shifts and bursting events. It is also shown that the dynamical trajectory passes close to equilibria that exhibit either low- or high-drag states. When statistics are collected at times where the friction velocity peaks, the mean flow and root-mean-square profiles show the essential features of wall turbulence obtained by DNS for the same friction Reynolds number. For low-drag events, the mean flow profiles are related to a universal asymptotic state called maximum drag reduction (Xi & Graham, Phys. Rev. Lett., vol. 108, 2012, 028301). Hence, the intermittent nature of self-sustaining processes in the buffer layer is contained in the dynamics of the RNL model, organized in two exact coherent states plus an asymptotic turbulent-like attractor. We also address how closely turbulent dynamics approaches these equilibria by exploiting a DNS database associated with a larger domain.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 864 , 10 April 2019 , pp. 221 - 243
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Copyright
© 2019 Cambridge University Press 

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