MHD Clumps: Heterogeneity and Radiative Cooling

We seek to understand the role magnetic field alignment and clump-clump spacing (filling fraction) have on the evolution of a host of randomly-distributed clumps overrun by a steady supersonic wind.

We do so by imposing a magnetic field in two configurations: parallel (Bx) and perpendicular (By) to the shock front, both with a plasma beta value of 1. We undertake an additional case in which there is no magnetic field, for comparison. We choose two configurations of clumps: sparse and dense, which are characterized by a filling fraction,

.\qquad\qquad f_{frac}=...$

Finally, we include the effects of radiative cooling. Based on \cite{Frank et al. 2011, Yirak et al. 2010} and references therein, we choose initial densities and temperatures such that both clump bow shocks and transmitted shocks have cooling time scales less than their respective dynamic timescales. In particular, the cloud-crushing time \citep{KMC94} given by

.\qquad\qquad t_{cc} = \frac{r_c}{\sqrt{\chi}v_s}$

where r_c is the radius of the clump, \chi the ratio of clump to preshock ambient density, and v_s the shock (wind) velocity.

As expected from \cite[][e.g.]{fragile2005, shin2008} and others, the Bx and hydro cases look relatively similar, while the By case is most disparate. Owing to stretching and bending of magnetic field lines, we find an amplification of field strength in _._._ of _._._. In case By, the shock speed is reduced by a factor of _._._, compared to _._._ for Bx (both relative to the hydro case).

We further discuss results below.

Note: I [Kris] am recalling the assignments below from memory so they may not be correct.

Hydro Case: Setting the Scene

Hydro sparse

Done: Brandon

movie​

Hydro dense

Done: Brandon

movie​

Bx Case: Strands Dominate

Bx sparse

Done: Shule

movie​

Bx dense

Done: Shule

movie​

By Case: Transitions to a Wall

By sparse

Jonathan: As of 12/20, needs roughly three weeks more for flow to reach edge of domain. At frame ~110 (out of an estimated 140).

movie​

• Click here for a discussion on the investigation of spurious artifacts in the By case with AMR.

By dense

Erica: Restarted from beginning with fixed grid. As of 12/20, produced about 150 frames in 4 days. Here is frame 154:

movie​

​http://support.mozilla.com/en-US/home?as=u

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Round II

After looking at the final frame of the By_sparse movie​

there were some striations - coming off of the magnetized rarefactions behind the clumps… To investigate this I ran a set of simulations focusing on the region around the clump at [8, 14.5]

Here is the same setup run out to frame 11. On the left is the density with field lines and on the right is the temperature. Notice the temperature protections in the magnetized rarefactions…

I then ran the same setup in fixed grid to ensure that AMR noise was not responsible

I then turned off the Local Oscillation Filter to see if that was reponsible

As well as switching from Characteristic limiters to primitive limiters

I then switched the interpolation order from 3 (PPM) to 1 (Gudonov)

And to order 2 (PLM)

Since lowering the order from 3 to 1 or 2 fixed the problem, i then checked that the Bx case also was well behaved

As well as the hydro case

And finally I checked that the HLLC solver gave the same result as the HLLD solver by turning of MHD

I suspect the same oscillations seen in 127 are behind the pressure protections - but I'm not entirely sure. —-​http://support.mozilla.com/en-US/home?as=uhttp://support.mozilla.com/en-US/home?as=uhttp://support.mozilla.com/en-US/home?as=uhttp://support.mozilla.com/en-US/home?as=uhttp://support.mozilla.com/en-US/home?as=uhttp://support.mozilla.com/en-US/home?as=uhttp://support.mozilla.com/en-US/home?as=u