Meeting Update 03/09/2015 - Eddie

I did some investigation into the intersection angles in my previous 2D Mach stem sims. I want to start thinking about the problem more time dependently.

Below is the gamma = 1.4, d = 5 simulation which results in a fairly wide Mach stem.

movie​

I think there is a good story here, and this is my interpretation:

  1. Bow shocks intersect.
  1. Bow shocks get "puffed" up due to increase in pressure in intersection region.
  1. The intersection angle crosses the minimum critical angle and a Mach stem forms.
  1. The Mach stem grows until the intersection angle hits the maximum critical angle.
  1. The Mach stem shrinks/grows a bit, almost like its breathing but it stays confined by the maximum critical angle.

Using this interpretation as a guide, I measured the relevant angles at different frames. I found that the angle right before Mach stem formation was about 42.75 deg (analytic theory says minimum should be 41.65 deg). Also, the intersection angle when the Mach stem stalls was about 58.33 deg (Pat's work says this maximum critical angle should be about 58.05 deg). This seems promising!

This seems like a good interpretation of the widest Mach stem scenario, but we need this to be consistent with the other models as well. There are 3 other possibilities:

  1. When the clumps are too close together, the Mach stem will grow beyond the maximum critical angle and disappear.
  1. For intermediate separations, the Mach stem does not always grow to the maximum angle. It can stop growing at some intermediate angle and be fairly stable. The d=5.5 model had a Mach stem that grew and stalled at an intersection angle of about 49.64 deg.
  1. For large separations, the intersection angle never gets above the minimum critical so a Mach stem cannot form.

Scenario 3 results in regular reflection, and we've seen that before. Scenarios 1 and 2 can be seen in the sims below:

movie​


3D Mach stems

I had to change the scale for the emission map with the M = 5 runs. There are some key differences here…

The Halpha is so weak that clearly the [S II] dominates. The Halpha maximum is only about twice as strong as the minimum, and the ambient is somewhere in between.

movie​

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