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Thin Shear Layers in High Reynolds Number Turbulence—DNS Results

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Abstract

Using direct numerical simulation of turbulence in a periodic box driven by homogeneous forcing, with a maximum of 40963 grid points and Taylor micro-scale Reynolds numbers R λ up to 1131, it is shown that there is a transition in the forms of the significant, high vorticity, intermittent structures, from isolated vortices when R λ is less than 102 to complex thin-shear layers when R λ exceeds about 103. Both the distance between the layers and their widths are comparable with the integral length scale. The thickness of each of the layers is of the order of the Taylor micro-scale λ. Across the layers the velocity ‘jumps’ are of the order of the rms velocity u o of the whole flow. Within the significant layers, elongated vortical eddies are generated, with microscale thickness ℓ v ~10η ≪ λ, with associated peak values of vorticity as large as 35ω rms and with velocity jumps as large as 3.4u o , where η is the Kolmogorov micro scale and ω rms the rms vorticity. The dominant vortical eddies in the layers, which are approximately parallel to the vorticity averaged over the layers, are separated by distances of order ℓ v . The close packing leads to high average energy dissipation inside the layer, as large as ten times the mean rate of energy dissipation over the whole flow. The interfaces of the layers act partly as a barrier to the fluctuations outside the layer. However, there is a net energy flux into the small scale eddies within the thin layers from the larger scale motions outside the layer.

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Authors and Affiliations

  1. Graduate School of Engineering, Nagoya University, Nagoya, 464-8603, Japan

    Takashi Ishihara

  2. Center for General Education, Aichi Institute of Technology, Toyota, 470-0392, Japan

    Yukio Kaneda

  3. Department of Earth Sciences, University College London, London, WC1E 6BT, UK

    Julian C. R. Hunt

  4. Trinity College, Cambridge, CB2 1TQ, UK

    Julian C. R. Hunt

Authors
  1. Takashi Ishihara
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  2. Yukio Kaneda
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  3. Julian C. R. Hunt
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Correspondence to Takashi Ishihara.

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Ishihara, T., Kaneda, Y. & Hunt, J.C.R. Thin Shear Layers in High Reynolds Number Turbulence—DNS Results. Flow Turbulence Combust 91, 895–929 (2013). https://doi.org/10.1007/s10494-013-9499-z

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