Scale-by-scale energy transfers and fluxes in compressible turbulence

¹ Department of Physics, Indian Institute of Technology Kanpur - Kanpur 208016, India
² Kotak School of Sustainability, Indian Institute of Technology Kanpur - Kanpur 208016, India

Received: 2 October 2025
Accepted: 28 April 2026

Abstract

Modeling atmospheric and stellar phenomena requires understanding compressive turbulence, a more complex problem than its incompressible counterpart. This paper employs a novel mathematical framework to analyze energy transfers and fluxes in subsonic compressible flows. We perform direct numerical simulations on a 1024³ grid for turbulent Mach numbers 0.15, 0.30, and 0.45. We apply stochastic random forcing to both rotational and compressive modes. We demonstrate that for subsonic flows, energy transfers from solenoidal to compressive modes are confined primarily to large scales, allowing independent rotational and compressive kinetic energy cascades. Consequently, both components maintain constant inertial-range fluxes, resulting in Kolmogorov scaling for the rotational velocity and Burgers scaling for the compressive velocity. We also observe that compressive kinetic energy is converted to internal energy via pressure dilatation. This advancement enables further exploration of locality, compressible convection, and compressible magnetohydrodynamics.