The statistics and structure of dissipation in subsonic and supersonic turbulence

TL;DR

This study investigates the structure and statistics of energy dissipation in subsonic and supersonic turbulence through high-resolution simulations, revealing different dissipation mechanisms and fractal properties across regimes.

Contribution

It provides new insights into the scale-dependent structure and statistical behavior of dissipation in turbulent flows, especially in astrophysical contexts.

Findings

Dissipation lags energy injection by ~1.6 and 0.5 turnover times in subsonic and supersonic turbulence.

In subsonic turbulence, dissipation correlates with vorticity; in supersonic, with density.

Achieving numerical convergence of dissipation across scales is challenging, especially in subsonic flows.

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 $1.64\pm0.21$ and $0.48\pm0.07$ turbulent turnover times in subsonic and supersonic turbulence, respectively. Correlations show $\varepsilon_{\mathrm{kin}}\propto\vert\nabla\times\mathbf{v}\vert^2$ (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. 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 $\varepsilon_{\mathrm{kin}}$. 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, $\varepsilon_{\mathrm{kin}}$ exhibits a fractal dimension between 1 and 2 across nearly all scales, likely reflecting shock surfaces and their intersections forming filaments.