Science Meeting Update 07/20/2014 - Eddie

For reference: ClumpClump/Morphology

Mainly just working on the Mach stem paper for the HEDLA proceedings. I hope to have it done within the next few days. I did some analysis on the shapes of the bow shocks from my simulations to confirm that they agree with the theory about Mach stem formation…

From analyzing the density maps, I was able to get a functional form for the bow shocks which end up looking like this:

Then, I can figure out what angle they would make if they intersected another bow shock. The theory of Mach stem formation says that they form at and above a critical angle which depends on gamma. For the values of gamma that I have used, these angles are:

gamma phi crit
5/3 74.75
1.4 83.31
1.2 95.34
1.01 137.46

Now, going back to the bow shock shape, I was able to pinpoint where these critical angles would occur. In other words, I figured out the critical separation distance for the 2 clumps at which Mach stems should begin to form. These are approximately:

gamma d crit
5/3 12.5
1.4 6.2
1.2 4.6
1.01 ?

I can't figure out d crit for the gamma = 1.01 case because the bow shock is unstable. The simulations are consistent with the theory because of which simulations we see Mach stems:

gamma d Mach stem?
5/3 15 no
5/3 10 yes
5/3 5 yes
1.4 10 no
1.4 5 yes
1.2 5 no

All simulated models not listed in the table above did not show evidence of a Mach stem.

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