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Journal Articles Journal of Fluid Mechanics Year : 2019

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

Damien Biau
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Abstract

A restricted nonlinear model, obtained by partitioning the state variables into stream-wise 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, p. 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, 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 dynamical trajectory passes close to equilibria that exhibit either low or high drag states. When statistics are collected at time where friction velocity peaks, mean flow and root mean square profiles show essential features of wall-turbulence obtained by DNS for the same friction Reynolds number. For low drag events, mean flow profiles are related to a universal asymptotic state called maximum drag reduction (Xi & Graham Phys. Rev. Letters, vol. 108, 2012, 028301). Hence, the intermittent nature of self-sustaining processes in the buffer layer is contained in the dynamics of 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 DNS database associated with a larger domain.
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Dates and versions

hal-02012878 , version 1 (09-02-2019)

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Frédéric Alizard, Damien Biau. Restricted nonlinear model for high and low drag events in a plane channel flow. Journal of Fluid Mechanics, 2019, 864, pp.221-243. ⟨10.1017/jfm.2019.14⟩. ⟨hal-02012878⟩
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