The statistics and structure of dissipation in subsonic and supersonic turbulence

ABSTRACT 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, $\varepsilon _{\mathrm{kin}}$, across subsonic and supersonic regimes. We find that dissipation lags large-scale kinetic energy injection events by $1.64\pm 0.21$ and $0.48\pm 0.07$ turbulent turnover times in subsonic and supersonic turbulence, respectively. Correlations show $\varepsilon _{\mathrm{kin}}\propto \vert \nabla \times \boldsymbol{v}\vert ^2$ (vorticity squared) in the subsonic regime, where density fluctuations are negligible, while in the supersonic regime dissipation is primarily correlated with density, $\varepsilon _{\mathrm{kin}}\propto \rho ^{3/2}$. A spectral analysis demonstrates that achieving numerical convergence of $\varepsilon _{\mathrm{kin}}$ across all scales is challenging, especially in the subsonic case, even at $2048^3$ resolution. None the less, subsonic dissipation is clearly localized 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 $\varepsilon _{\mathrm{kin}}$. In the subsonic regime, intense dissipation is predominantly organized in flattened vortex filaments embedded in thin shearing layers on small scales, becoming more volume-filling at larger scales. In the supersonic regime, $\varepsilon _{\mathrm{kin}}$ exhibits a fractal dimension between 1 and 2 across nearly all scales, likely reflecting shock surfaces and their intersections forming filaments.