The Origin of Da Scaling: Suppressed Cooling in Fast-Cooling Mixing Layers

Abstract: In numerical experiments simulating Turbulent Radiative Mixing Layers (TRMLs) it is observed that as the cooling time in the mixed gas, $t_{\rm cool}$, becomes very short compared to the dynamical time of the turbulence, $t_{\rm eddy}/t_{\rm cool} \gg 1$, there is a change in the scaling behavior of the total energy radiated in the TRML as a function of this ratio, also known as the Damköhler number, ${\rm Da} \equiv t_{\rm eddy}/t_{\rm cool}$, from $\dot{E}<em>{\rm cool} \propto {\rm Da}<sup>{1/2}$ to $\dot{E}</em>{\rm cool} \propto {\rm Da}<sup>{1/4}$. The latter, so-called "fast-cooling," regime is of particular interest as many astrophysical mixing layers lie in this regime. We demonstrate that the origin of this change is the suppression of turbulent folding of the surface by the ram-pressure of the inflowing gas, which becomes much greater than the turbulent pressure in this regime. We present an argument that reproduces the $\dot{E}_{\rm cool} \propto {\rm Da}<sup>{1/4}$ behavior by appealing to the suppression of the fractal structure of the interface by the ram-pressure of the inflowing gas.