  Radiative mixing layers arise wherever multiphase gas, shear, and radiative
cooling are present. Simulations show that in steady state, thermal advection
from the hot phase balances radiative cooling. However, many features are
puzzling. For instance, hot gas entrainment appears to be numerically converged
despite the scale-free, fractal structure of such fronts being unresolved.
Additionally, the hot gas heat flux has a characteristic velocity $v_{\rm in}
\approx c_{\rm s,cold} (t_{\rm cool}/t_{\rm sc,cold})^{-1/4}$ whose strength
and scaling are not intuitive. We revisit these issues in 1D and 3D
hydrodynamic simulations. We find that over-cooling only happens if numerical
diffusion dominates thermal transport; convergence is still possible even when
the Field length is unresolved. A deeper physical understanding of radiative
fronts can be obtained by exploiting parallels between mixing layers and
turbulent combustion, which has well-developed theory and abundant experimental
data. A key parameter is the Damk\"ohler number ${\rm Da} = \tau_{\rm
turb}/t_{\rm cool}$, the ratio of the outer eddy turnover time to the cooling
time. Once ${\rm Da} > 1$, the front fragments into a multiphase medium. Just
as for scalar mixing, the eddy turnover time sets the mixing rate, independent
of small scale diffusion. For this reason, thermal conduction often has limited
impact. We show that $v_{\rm in}$ and the effective emissivity can be
understood in detail by adapting combustion theory scalings. Mean density and
temperature profiles can also be reproduced remarkably well by mixing length
theory. These results have implications for the structure and survival of cold
gas in many settings, and resolution requirements for large scale galaxy
simulations.
