Progress as of 19 November 2020

These first plots are taken from one-dimensional runs. These plots trace the position of the shock front as it moves through time. The red curve is taken as the point of maximum temperature, while the blue curve is taken as the point of steepest increase in the logarithm of density. On the right of each of these is the Fourier transform of the temperature plot. In cases where the temperature is constant throughout (which occurs if the shock isn't fully resolved; this only seems to occur for negative values of beta) the peak temperature location is taken to be the location of the previous peak.

It should be noted that there are usually two regions of high density increase; the forward of which usually coincides with temperature peak while the rear usually coincides with the point where temperature returns to the ambient value. The steeper of the two is usually, but not necessarily, the rear. This explains some of the sharp oscillations observed in the higher values of beta as the front gradient becomes as steep as the rear.

Beta Position Fourier Transform
-1.0
-0.5
0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0

These next sets switch to three dimensions, all using Beta=0 (constant cooling function). From left to right, the (estimated) cooling length is set to be approximately equal to five jet radii, one jet radius, half the jet radius, one fourth, and one eighth.

First a slice of density

Next a slice of temperature

A projection of density

And another projection along the jet axis

Currently I am conducting runs with varying Beta, using the same value of alpha that produced the cooling length equal to five jet radii and all of the values of beta that were used in the one-dimensional runs. These runs are also conducted over a larger area. So far I have preliminary results for Beta=1 (Left) and Beta=2 (Right)

Slice of density

Slice of temperature

Projection of density

Projection along the jet axis

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