Invariant solutions of minimal large-scale structures in turbulent channel flow for Reτ up to 1000

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Title: Invariant solutions of minimal large-scale structures in turbulent channel flow for Reτ up to 1000
Authors: Hwang, Y
Willis, AP
Cossu, C
Item Type: Journal Article
Abstract: Understanding the origin of large-scale structures in high Reynolds number wall turbulence has been a central issue over a number of years. Recently, Rawat et al. (J. Fluid Mech., 2015, 782, p515) have computed invariant solutions for the large-scale structures in turbulent Couette flow at Reτ ≃ 128 using an over-damped LES with the Smagorinsky model to account for the effect of the surrounding small-scale motions. Here, we extend this approach to an order of magnitude higher Reynolds numbers in turbulent channel flow, towards the regime where the large-scale structures in the form of very-large-scale motions (long streaky motions) and large-scale motions (short vortical structures) energetically emerge. We demonstrate that a set of invariant solutions can be computed from simulations of the self-sustaining large-scale structures in the minimal unit (domain of size Lx = 3.0h streamwise and Lz = 1.5h spanwise) with midplane reflection symmetry at least up to Reτ ≃ 1000. By approximating the surrounding small scales with an artificially elevated Smagorinsky constant, a set of equilibrium states are found, labelled upper- and lower-branch according to their associated drag. It is shown that the upper-branch equilibrium state is a reasonable proxy for the spatial structure and the turbulent statistics of the self-sustaining large-scale structures.
Issue Date: 1-Aug-2016
Date of Acceptance: 8-Jul-2016
URI: http://hdl.handle.net/10044/1/34701
DOI: https://dx.doi.org/10.1017/jfm.2016.470
ISSN: 1469-7645
Publisher: Cambridge University Press (CUP)
Journal / Book Title: Journal of Fluid Mechanics
Volume: 802
Copyright Statement: The final publication is available via Cambridge Journals Online at http://dx.doi.org/10.1017/jfm.2016.470
Sponsor/Funder: Engineering and Physical Sciences Research Council
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/N019342/1
EP/N019342/1
Keywords: Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
low-dimensional models
nonlinear dynamical systems
turbulent boundary layers
EXACT COHERENT STRUCTURES
PLANE COUETTE TURBULENCE
TRAVELING-WAVE SOLUTIONS
PIPE-FLOW
BOUNDARY-LAYERS
WALL TURBULENCE
STATE-SPACE
TRANSITION
MOTIONS
SIMULATION
Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Article Number: R1
Appears in Collections:Faculty of Engineering
Aeronautics



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