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arXiv · 2508.04300

Mathematical formulation of mode-to-mode energy transfers and energy fluxes in compressible turbulence

Dhananjay Singh·Harshit Tiwari·Lekha Sharma·Mahendra K. Verma
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Abstract

Understanding compressible turbulence is critical for modeling atmospheric, astrophysical, and engineering flows. However, compressible turbulence poses a more significant challenge than incompressible turbulence. We present a novel mathematical framework to compute \textit{mode-to-mode energy transfer rates} and energy fluxes for compressible flows. The formalism captures detailed energy conservation within triads and allows decomposition of transfers into rotational, compressive, and mixed components, providing a clear picture of energy exchange among velocity and internal energy modes. We also establish analogies with incompressible hydrodynamic and magnetohydrodynamic flows, highlighting the framework's universality in studying energy transfers.

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Dhananjay Singh, Harshit Tiwari, Lekha Sharma, Mahendra K. Verma. 2025-08-06. Mathematical formulation of mode-to-mode energy transfers and energy fluxes in compressible turbulence. https://arxiv.org/abs/2508.04300

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