Universal Structure of Turbulent Radiative Mixing Layers

Abstract

Turbulent radiative mixing layers (TRMLs), where shear-driven turbulence between dense and diffuse gas produces rapidly cooling intermediate-temperature gas, are ubiquitous in the interstellar and circumgalactic media. Using a quasi-steady Reynolds decomposition, we separate mean and turbulent components. In quasi-isobaric TRMLs, upstream gas cools and compresses before streamwise momentum is fully mixed, yielding a negative shear stress (R_{xz}) and a positive compressive stress (R_{zz}) that together sustain a steady radiative conversion of hot to cold gas. A pronounced thermal-pressure dip develops within the TRML, while radiative losses are offset by the divergences of enthalpy flux and (subdominant) turbulent heat flux (Q_t). The volume-averaged temperature follows a tanh profile, resulting in universal emissivity distributions that are consistent with simulations. Contrary to previous claims, the cooling-rate surface density saturates and becomes independent of box size in the strong-cooling limit, establishing the universal structure of TRMLs.

Figures (4)

• Figure 1: Snapshots showing density, pressure, cooling time, and velocity fluctuations in the quasi-steady TRML. Diffuse hot gas collapses quasi-isobarically through a thin fractal cooling interface. Vertical motions dissipate inside the TRML, while streamwise momentum penetrates deeper into the cold phase. The pressure dip and compressive collapse inside the TRML are clearly visible.
• Figure 2: Mean vertical profiles of density, velocity components, temperature, and conserved fluxes in steady state. Shaded bands indicate $1\sigma$ temporal variability. Turbulent contributions to mass and energy fluxes are confined to the TRML, while the x-momentum flux progressively penetrates into the cold phase. The temperature profile is well fit by a tanh function. Long temporal averaging suppresses transient acoustic fluctuations, isolating the quasi-steady structure.
• Figure 3: Normalized volume, mass, and emissivity PDFs (${\cal P}[\log_{10}T]$) across temperature within the TRML, restricted to $[1.1T_c,0.9T_h]$ where the mean temperature profile is well described by Eq. \ref{['eq:tanh_T']}. Solid lines show simulation results (shaded bands: temporal $1\sigma$ variations); dashed lines show analytic predictions based on Eq. \ref{['eq:PV_to_PMPE']} and the $\tanh$ fit to ${\overline{\cal P}}_V(\langle T \rangle)$, which remarkably also fits ${\cal P}_V(T)$. In the turbulent steady state, $P_{V,M,E}[T]$ show only tiny variations in time for all the resolved runs. For comparison, the red dashed line shows the distinct prediction for ${\cal P}_E$ from a non-turbulent, steady cooling flow. The purple line denotes the emissivity PDF across horizontally averaged temperature, distinct from the emissivity PDF across physical temperature.
• Figure 4: The balance of radiative cooling losses $\langle n^2 \Lambda \rangle$, divergence of enthalpy flux ($d[\langle {\cal B} \rangle \langle \rho u_z \rangle]/dz$), and turbulent heat transport ($d[\langle \delta {\cal B} \delta \rho u_z \rangle]/dz$) within the TRML. Solid lines are based on simulation data and dashed lines on the theoretical model (Eqs. \ref{['eq:tanh_T']}, \ref{['eq:Q_t_closure_int']}). The dotted line for turbulent heating is based on a simple closure ${\cal Q}_t = - \kappa_t d\langle T \rangle/dz$ with $\kappa_t = 0.1 k_B \rho_h \Delta u^2 t_0 /(\mu m_p)$.