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Nonlinear Transverse Cascade—A Key Factor of Sustenance of Subcritical Turbulence in Shear Flows

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Turbulent Cascades II

Part of the book series: ERCOFTAC Series ((ERCO,volume 26))

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Abstract

We analyze the essence of nonlinear processes that underlie turbulence sustenance in spectrally stable shear flows. In these flows, the strong anisotropy of velocity shear-induced nonmodal growth phenomenon in spectral (k-)space, in turn, entails the anisotropy of nonlinear processes in this space. Consequently, the main novel nonlinear process is transverse, or angular redistribution of modes in Fourier space referred to as the nonlinear transverse cascade rather than a mere direct/inverse cascade. It is demonstrated that nonlinear coherent as well as turbulent states are sustained via a subtle interplay of the linear nonmodal growth (that has transient nature) and the nonlinear transverse cascade. This course of events exemplifies the well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. In this proceedings paper, we present selected results of our simulations of hydrodynamic and MHD 2D plane shear flows to demonstrate the transverse cascade in action.

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Acknowledgements

D. G. acknowledges the financial support from the US Department of Energy under grant DE-FG02-04ER54742; G. M. is supported by the Alexander von Humboldt Foundation (Germany).

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Authors and Affiliations

  1. Department of Physics, The University of Texas at Austin, Austin, TX, 78712, USA

    D. Gogichaishvili

  2. Helmholtz-Zentrum Dresden-Rossendorf, P.O. Box 510119, 01314, Dresden, Germany

    G. Mamatsashvili

  3. Abastumani Astrophysical Observatory, Ilia State University, 0162, Tbilisi, Georgia

    G. Chagelishvili

  4. Institute of Geophysics, Tbilisi State University, 0193, Tbilisi, Georgia

    G. Chagelishvili

  5. Institute for Fusion Studies, The University of Texas at Austin, Austin, TX, 78712, USA

    W. Horton

Authors
  1. D. Gogichaishvili
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  2. G. Mamatsashvili
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  3. G. Chagelishvili
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  4. W. Horton
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Corresponding author

Correspondence to D. Gogichaishvili .

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Editors and Affiliations

  1. Laboratoire de Mécanique des Fluides et d’Acoustique CNRS, Université de Lyon, École centrale de Lyon, Écully, France

    Mikhael Gorokhovski

  2. Laboratoire de Mécanique des Fluides et d’Acoustique CNRS, Université de Lyon, École centrale de Lyon, Écully, France

    Fabien S. Godeferd

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Gogichaishvili, D., Mamatsashvili, G., Chagelishvili, G., Horton, W. (2019). Nonlinear Transverse Cascade—A Key Factor of Sustenance of Subcritical Turbulence in Shear Flows. In: Gorokhovski, M., Godeferd, F. (eds) Turbulent Cascades II. ERCOFTAC Series, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-030-12547-9_12

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  • DOI: https://doi.org/10.1007/978-3-030-12547-9_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12546-2

  • Online ISBN: 978-3-030-12547-9

  • eBook Packages: EngineeringEngineering (R0)

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