Universal Structure of Turbulent Radiative Mixing Layers

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.