Cloud crushing in a spherical box

SphericalBoxCC.md

Chevalier & Clegg 1985 (CC85) wind is spherically symmetric. So a coordinate system in the simulation that naturally aligns with the wind geometry allows the steady wind profiles to remain numerically stable for an arbitrarily long time. Therefore, it is worth setting cloud crushing problem in spherical coordinates to study it cloud-wind interaction in an adiabatically expanding wind, like CC85.

To retain the hierarchy that wind corresponds to hot gas and mixed gas has an intermediate temperature between cold cloud and the wind. The physically relevant portion of the domain where the general cloud crushing results are applicable is where $T_{\rm wind} \ge T_{\rm mix}$, where $T_{\rm mix} = T_{\rm wind}/\sqrt{\chi}$, and $\chi$ is the initial temperature contrast between the wind and the cloud.

Here is the entire simulation domain where the code length is the initial cloud radius. For this visualization, I have chosen $t_{\rm cool, mix}/t_{\rm cc}=0.1$. This corresponds to one of the largest clouds in the simulation suite and is found to be rapidly growing in vanilla cloud crushing (plane-parallel).

Here are slice plots of cooling times in Myr and the ratio $t_{\rm cool}/t{\rm sc}$, respectively. For calculating $t_{\rm sc}$ here, I'm using the distance as cell_volume$^{1/3}$. Perhaps, you can see a small circle (a little bit hard to see!) near the left edge of the slice plot, which is the cold and dense spherical cloud.

Now, I'm choosing a sub-domain where $T_{\rm wind} \ge T_{\rm mix}$. This is shown next with respect to the entire simulation domain.

Let's re-plot the same quantitites inside the sub-domain. Here, the sub-domain is a zoomed-in region, where the cloud is much more prominent.

Next I'm adding in the evolution of slice plots of a few relevant fluid fields. Each frame in the snapshots are $1\ t_{\rm cc}$ apart from the next.

The mass evolution for clouds of different sizes which is inversely proportional to the ratio $t_{\rm cool, mix}/t_{\rm cc}$ is as follows. Here the distance travelled by the center of mass of the cloud with respect to its initial position from the wind center is denoted by $d_{\rm cl}/d_{\rm cl, ini}$