4.7 Article

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

Journal

JOURNAL OF FLUID MECHANICS
Volume 802, Issue -, Pages -

Publisher

CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2016.470

Keywords

low-dimensional models; nonlinear dynamical systems; turbulent boundary layers

Funding

  1. Engineering and Physical Sciences Research Council (EPSRC) in the UK [EP/N019342/1]
  2. EPSRC [EP/L000261/1, EP/N019342/1] Funding Source: UKRI
  3. Engineering and Physical Sciences Research Council [EP/L000261/1, EP/N019342/1] Funding Source: researchfish

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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., vol. 782, 2015, pp. 515-540) have computed invariant solutions for the large-scale structures in turbulent Couette flow at Re-tau similar or equal to 128 using an overdamped large-eddy simulation with the Smagorinsky model to account for the effect of the surrounding small-scale motions. Here, we extend this approach to Reynolds numbers an order of magnitude higher 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) emerge energetically. 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 L-x, = 3.0h streamwise and L-z =1.5h spanwise) with midplane reflection symmetry at least up to Re-tau similar or equal to 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.

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