Restricted nonlinear model for high and lowdrag events in plane channel flow
Article dans une revue avec comité de lecture
Date
2019Journal
Journal of Fluid MechanicsAbstract
A restricted nonlinear (RNL) model, obtained by partitioning the state variables into streamwiseaveraged 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 streamwiseaveraged 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 highdrag states. When statistics are collected at times where the friction velocity peaks, the mean flow and rootmeansquare profiles show the essential features of wall turbulence obtained by DNS for the same friction Reynolds number. For lowdrag 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 selfsustaining processes in the buffer layer is contained in the dynamics of the RNL model, organized in two exact coherent states plus an asymptotic turbulentlike attractor. We also address how closely turbulent dynamics approaches these equilibria by exploiting a DNS database associated with a larger domain.
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