E vs. t Line Plots

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Total energy v time plots were made in Visit using a cylinder clip operator and the query summing function,

We varied the size of the 'collision region' we were integrating through to account for the shear angle,

\theta	Lx	Ly = Lz
0	20 pc	40 pc
15	NA	NA
30	NA	NA
60	NA	NA

The expressions in Visit were:

Kinetic Energy	.5*rho(vx2+vy2+vz2)
Magnetic Energy	.5(B2)
Gravitational Energy	gas phi*rho

The gravitational energy computed this way neglects particle-gas interactions, and so is an approximation to the total gravitational energy of the collision region.

Below are a series of simple line plots for particular energies over time in our colliding flows runs (all beta = 0, for varying shear angles (0 (No Shear), 15, 30, and 60). The energies we are plotting are defined below. The independent variable on these plots is the time in Myr for the ratio of the energy at a particular time over the initial energy at t = 0 Myr. Hence we see that each plot is normalized at 1 on the dependent axis. Here I will describe the process of how we acquired these plots.

The equations used to define these quantities are the following:

Kinetic Energy

T = \frac{1}{2}\rho \left(v_{x}^2 + v_{y}^2 + v_{z}^2\right)

As a mathematical expression in VisIt: .5*rho*(vx^2 + vy^2 + vz^2)

• \rho is the density
• v_{i} are the cartesian components of the 3-dimensional velocity vector

Gravitational Energy

E_{\text{grav}} = \frac{1}{2}\phi_{\text{gas}}\rho

As a mathematical expression in VisIt: .5*<Gas Phi>*rho

• \rho is the density
• \phi_{\text{gas}} is the potential due to the gas

Magnetic Energy

E_{\text{mag}} = \frac{1}{2}\left(B_{x}^2 + B_{y}^2 + B_{z}^2\right)

As a mathematical expression in VisIt: .5*(Bx^2 + By^2 + Bz^2)

• All B_{i} are the cartesian components of the 3-dimensional magnetic field vector

Firstly note that each run has different box sizes. We have "small box" and a "large box" runs. The shear 0 and 15 data sets have a small box size, i.e. (x, y, z) = (62.5, 75 75), where as 30 and 60 have a larger box, i.e. (x, y, z) = (200, 75, 75). We have chosen these parameters given the size of the collision is dependent on the size of the shear angle.

We want to be able to extract the energies in the collision region, so we need to "clip" the HDF5 file in VisIt that contains our data. We use this using the box operator on our data. The clipped box should be 40 pc in y and z to fulling encompass the cylindrical collision region. However since our box varies in x, we need to clip the box differently for each run. For shear 0 and 15 we clipped the simulation box for 20 pc. On the other hand we clipped the shear 30 case by 24 pc, and shear 60 for 70 pc. To do this you take the length of one of the parameters of the box, half it, and then consider that maximum and minimum using the box operator.

To pick up the values for the energies simply create expressions for them (see above) in VisIt. Then go to Query > Weighted Variable Query. Then you can find the value for particular times. Here we sampled each run for the following frames: 0, 101, 202, 273 (and 328 for shear 60). The data was sampled with 3 levels of amr.

E vs. t Plots Table

You can find a discussion of the E vs. t plots on this ​page.

	Shear 0	Shear 15	Shear 30	Shear 60
Gravitational Energy
Other Energies

Beta 10, Shear 0

Initial Values

Magnetic Energy	1.78E+07
Kinetic Energy	1.79E+08
Gravitational Energy	-2.03E+06

Tabled Data

Magnetic Energy	E/Einit	Grav.	E/Einit	Kin	E/Einit	Time	Time (Myr)
1.78E+07	1.00E+00	-2.03E+06	1.00E+00	1.79E+08	1	0	0
2.25E+07	1.26E+00	-2.38E+07	1.17E+01	2.05E+08	1.14E+00	0.83325	9.999
2.30E+07	1.29E+00	-2.44E+07	1.20E+01	2.16E+08	1.20E+00	1.6665	19.998
2.36E+07	1.32E+00	-2.47E+07	1.21E+01	2.16E+08	1.21E+00	2.25	27

Beta 10, Shear 15

Initial Values

Magnetic Energy	1.76E+07
Kinetic Energy	1.77E+08
Gravitational Energy	-2.00E+06

Tabled Data

Magnetic Energy	E/Einit	Grav.	E/Einit	Kin	E/Einit	Time	Time (Myr)
1.76E+07	1.00E+00	-2.00E+06	1.00E+00	1.77E+08	1	0	0
2.15E+07	1.23E+00	-2.51E+07	1.26E+01	2.06E+08	1.17E+00	0.83325	9.999
2.23E+07	1.27E+00	-2.51E+07	1.25E+01	2.18E+08	1.23E+00	1.6665	19.998
1.85E+07	1.06E+00	-2.11E+07	1.06E+01	2.17E+08	1.23E+00	2.25	27

Beta 10, Shear 30

Initial Values

Magnetic Energy	2.02E+07
Kinetic Energy	2.04E+08
Gravitational Energy	-3.42E+06

Tabled Data

Magnetic Energy	E/Einit	Grav.	E/Einit	Kin	E/Einit	Time	Time (Myr)
2.02E+07	1.00E+00	-3.42E+06	1.00E+00	2.04E+08	1	0	0
2.84E+07	1.40E+00	-2.55E+07	7.46E+00	2.44E+08	1.20E+00	0.83325	9.999
3.07E+07	1.52E+00	-3.41E+07	9.97E+00	2.53E+08	1.24E+00	1.6665	19.998
2.93E+07	1.45E+00	-3.36E+07	9.83E+00	2.54E+08	1.24E+00	2.25	27

Beta 10, Shear 60

Initial Values

Magnetic Energy	1.14E+08
Kinetic Energy	1.16E+09
Gravitational Energy	-1.37E+07

Tabled Data

Magnetic Energy	E/Einit	Grav.	E/Einit	Kin	E/Einit	Time	Time (Myr)
1.14E+08	1.00E+00	-1.37E+07	1.00E+00	1.16E+09	1	0	0
1.18E+08	1.04E+00	-2.39E+07	1.75E+00	1.27E+09	1.09E+00	0.83325	9.999
1.31E+08	1.14E+00	-3.44E+07	2.52E+00	1.23E+09	1.06E+00	1.6665	19.998
1.31E+08	1.15E+00	-4.12E+07	3.01E+00	1.25E+09	1.08E+00	2.25	27
1.32E+08	1.15E+00	-4.26E+07	3.12E+00	1.23E+09	1.06E+00	2.796	33.552