The statistics and structure of dissipation in subsonic and supersonic turbulence

Turbulence plays a critical role in the atmosphere, oceans, engineering, and astrophysics. The dissipation (heating) induced by turbulent flows is particularly important for the thermodynamics and chemistry of interstellar clouds, yet its structure and statistics remain poorly understood. Using high-resolution turbulence simulations with controlled explicit viscosity, we study the kinetic energy dissipation rate, ϵkin, across subsonic and supersonic regimes. We find that dissipation lags large-scale kinetic energy injection events by 1.64 ± 0.21 and 0.48 ± 0.07 turbulent turnover times in subsonic and supersonic turbulence, respectively. Correlations show ϵkin∝|∇ × v|2 (vorticity squared) in the subsonic regime, where density fluctuations are negligible, while in the supersonic regime dissipation is primarily correlated with density, ϵkin∝ρ3/2. A spectral analysis demonstrates that achieving numerical convergence of ϵkin across all scales is challenging, especially in the subsonic case, even at 20483 resolution. Nonetheless, subsonic dissipation is clearly localised on small vorticity-dominated scales, while supersonic dissipation spans many scales, combining elongated, thin shocks with small-scale vorticity. Finally, we determine the fractal dimension of ϵkin. In the subsonic regime, intense dissipation is predominantly organised in flattened vortex filaments embedded in thin shearing layers on small scales, becoming more volume-filling at larger scales. In the supersonic regime, ϵkin exhibits a fractal dimension between 1 and 2 across nearly all scales, likely reflecting shock surfaces and their intersections forming filaments.