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Energy Spectra and Fluxes in Dissipation Range of Turbulent and Laminar Flows

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Abstract

Two well-known turbulence models to describe the energy spectrum in the inertial and dissipative ranges simultaneously are by Pao (1965) and Pope (2000). In this paper, we compute energy spectrum E(k) and energy flux Π(k) using direct numerical simulations on grids up to 40963, and show consistency between the numerical results and predictions by the aforementioned models for turbulence flows. We also consider the laminar flow in which viscosity dominates over nonlinearity. For this case we suggest a modified model that predicts E(k) ~ k−1 exp(−k) and Π(k) ~ k exp(−k) in dissipation range of scales and verify it using numerical simulations. We emphasize the difference revealing local energy transfer for the turbulent flows and nonlocal one for the laminar flows at low Reynolds number.

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Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology, Kanpur, 208016, India

    M. K. Verma, A. Kumar, P. Kumar, S. Barman & A. G. Chatterjee

  2. Mechanical Engineering, Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Kingdom of Saudi Arabia

    R. Samtaney

  3. Institute of Continuous Media Mechanics, Korolev 1, Perm, 614013, Russia

    R. A. Stepanov

Authors
  1. M. K. Verma
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  2. A. Kumar
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  3. P. Kumar
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  4. S. Barman
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  5. A. G. Chatterjee
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  6. R. Samtaney
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  7. R. A. Stepanov
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Correspondence to M. K. Verma.

Additional information

Original Russian Text © M.K. Verma, A. Kumar, P. Kumar, S. Barman, A.G. Chatterjee, R. Samtaney, R.A. Stepanov, 2018, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2018, No. 6, pp. 142–154.

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Verma, M.K., Kumar, A., Kumar, P. et al. Energy Spectra and Fluxes in Dissipation Range of Turbulent and Laminar Flows. Fluid Dyn 53, 862–873 (2018). https://doi.org/10.1134/S0015462818050166

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  • DOI: https://doi.org/10.1134/S0015462818050166

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