edit to mach stem runs

I looked at Kris' paper on mach stems and hysteresis: ​http://adsabs.harvard.edu/abs/2013HEDP....9..251Y

Here they labeled the critical angle as the angle that the bow shock makes with a vertical line, not the included angle between the bow shocks. So my previous calculations to find the critical separation distance were actually using the wrong angle.

With this correction, the critical separations decreased. Unfortunately, some of them decreased to the point where it would be difficult to simulate. In other words, when the critical separation gets really close to 2 rclump it becomes difficult to put the clumps close together below critical because the clumps would overlap. So I had to change my runs to be 5% above and 5% below critical instead of 10% like I had before. Below is the corrected table with the grid domain and resolution for each of my runs:

Run Mach Stem? Domain Size (x, y, z) Base Grid (mx, my, mz)
A no 1.243, 2.486, 0.6215 6, 12, 3 ←— lowest physical resolution at 77 cells/rclump
B yes 1.125, 2.250, 0.5625 6, 12, 3
C no 1.205, 2.410, 0.6025 6, 12, 3
D yes 1.090, 2.180, 0.545 6, 12, 3
E no 1.168, 2.336, 0.584 6, 12, 3
F yes 1.057, 2.114, 0.5285 6, 12, 3
G no 1.143, 2.286, 0.5715 6, 12, 3
H yes 1.034, 2.068, 0.517 6, 12, 3 ←— highest physical resolution at 92 cells/rclump

According to these numbers, the run that I showed yesterday should not have formed a mach stem. It was at x = 1.242 which is pretty close to what I am now calling run A. Perhaps what we saw was something non-physical due to some boundary effects. I am rerunning that set up with the lower y boundary extended.

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