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Energy Transfer and Spectra in Simulations of Two-Dimensional Compressible Turbulence

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Turbulent Cascades II

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

Abstract

We present results of high-resolution numerical simulations of compressible 2D turbulence forced at intermediate spatial scales with a solenoidal white-in-time external acceleration. A case with an isothermal equation of state, low energy injection rate, and turbulent Mach number \(M\approx 0.34\) without energy condensate is studied in detail. Analysis of energy spectra and fluxes shows that the classical dual-cascade picture familiar from the incompressible case is substantially modified by compressibility effects. While the small-scale direct enstrophy cascade remains largely intact, a large-scale energy flux loop forms with the direct acoustic energy cascade compensating for the inverse transfer of solenoidal kinetic energy. At small scales, the direct enstrophy and acoustic energy cascades are fully decoupled at small Mach numbers and hence the corresponding spectral energy slopes comply with theoretical predictions, as expected. At large scales, dispersion of acoustic waves on vortices softens the dilatational velocity spectrum, while the pseudo-sound component of the potential energy associated with coherent vortices steepens the potential energy spectrum.

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Acknowledgements

This research was supported in part by the National Science Foundation through Grant No. AST-1412271 as well as through XSEDE allocation MCA07S014 on Stampede-1/2 at TACC (production runs) and on Comet at SDSC (data analysis).

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Authors and Affiliations

  1. University of California, San Diego, USA

    Alexei G. Kritsuk

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  1. Alexei G. Kritsuk
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Correspondence to Alexei G. Kritsuk .

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  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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Kritsuk, A.G. (2019). Energy Transfer and Spectra in Simulations of Two-Dimensional Compressible Turbulence. 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_8

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  • DOI: https://doi.org/10.1007/978-3-030-12547-9_8

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