Energy transfer across scales in a shock: is it a scale-local cascade?

ORAL

Abstract

It is commonly claimed that kinetic energy (KE) in the presence of a shock does not undergo an inertial scale-local cascade but that KE at a given scale must be dissipated directly into heat at the viscous (molecular) scales without passing through intermediate scales. Using rigorous mathematical analysis and physical arguments, we will explain why this widely held notion rests on flawed/unrefined intuition. We demonstrate rigorous proofs of scale-locality of the cascade due to shocks using two examples: (i) Burgers equation and (ii) exact 1D normal shock solution. Our analytical results hold in broad generality, for turbulence at any Mach number, for any equation of state, and without the requirement of homogeneity or isotropy. The assumptions we make in our proofs on the scaling of velocity, pressure, and density structure functions are weak and enjoy compelling empirical support.

*This research was supported by US DOE grant DE-SC0020229 and NSF grant PHY-2206380. Partial support from US NSF grants PHY-2020249 is acknowledged.

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Presenters

  • Dina Soltani Tehrani

    • Dept. of Mechanical Eng., University of Rochester, NY, USA

Authors

  • Dina Soltani Tehrani

    • Dept. of Mechanical Eng., University of Rochester, NY, USA

  • Hussein Aluie

    • Dept. of Mechanical Engg, University of Rochester
    • Dept. of Mechanical Engg, University of Rochester. Laboratory for Laser Energetics, Rochester, NY, USA.
    • Dept. of Mechanical Eng, University of Rochester. Laboratory for Laser Energetics, Rochester, NY, USA.