wiki:MachStems

Version 34 (modified by ehansen, 9 years ago) ( diff )

Mach Stems


2D Stationary Clumps

This problem set up has bow shocks from two identical, stationary clumps. I test different gammas and different separation distances. To reduce computation, I am only using one clump with a reflecting wall on the lower r boundary to simulate the second clump's bow shock. I also only simulate ¼ of the clump due to symmetry. In the context of this problem, critical separation distance is equivalent to 2 times the critical radius.

Thinking in terms of critical radius versus critical angle can get confusing. Traditionally, we think of mach stem formation in terms of critical angle. Anything above this angle means a mach stem will form. The critical angle corresponds to a critical radius, but now we must remember that anything below this radius means a mach stem will form.

Below is a table of the resolutions used for all of the runs. These were determined by keeping the proportions of the domain constant and shooting for a minimum of 32 cells per clump radius. As a result of doing it this way, some runs will have higher resolution, but it basically stays between 32 and 38 cells per clump radius. For the 'lower r boundary' column, crit = critical, acrit = above critical, bcrit = below critical. Mach stems should form at crit and bcrit, but not at acrit.

gamma lower r boundary Base Grid (r,z) [cells] Domain Size (r,z) [cu] Cells / Rclump
1.6667 crit 12, 18 1.46, 2.19 32.88
1.6667 acrit 14, 21 1.66, 2.49 33.73
1.6667 bcrit 12, 18 1.26, 1.89 38.10
1.4 crit 12, 18 1.39, 2.085 34.53
1.4 acrit 14, 21 1.59, 2.385 35.22
1.4 bcrit 10, 15 1.19, 1.785 33.61
1.2 crit 12, 18 1.32, 1.98 36.36
1.2 acrit 14, 21 1.52, 2.28 36.84
1.2 bcrit 10, 15 1.12, 1.68 35.71
1.1 crit 12, 18 1.27, 1.905 37.80
1.1 acrit 12, 18 1.47, 2.205 32.65
1.1 bcrit 10, 15 1.07, 1.605 37.38


gamma = 1.6667

left boundary Image Movie
bcrit movie
crit movie
acrit movie


gamma = 1.4

movie


3D Runs

Simulation Setups

All simulations are done in a reference frame moving at M = 7. Simulation times are shown in computation units, but the total physical time is approximately 75 years.

2-clump setup (runs A - F): Clumps separated by a distance d measured in clump radii. Clump velocities given in terms of their Mach numbers.

3-clump setup (runs G - L): See diagrams below. The clumps are labeled by their Mach numbers. The clump separation d (measured in clump radii) and angle a are the defining parameters that change for each run. The point labeled O marks the location of the observer from which a line of sight is drawn to generate the emission maps. The position of the observer is determined by two angles: the rotation angle phi is denoted in the top view diagram, and the inclination angle i is denoted in the side view diagram.

No image "3clumpsetup.png" attached to MachStems

multi-clump setup (run M): In x and z, the clumps are arranged in a 3-4-3 lattice-like structure. Each clump is given a random position in y and an appropriate velocity based on that y-position so that the clump does not run off the grid during the simulation.

Run # Clumps Defining parameters Machine Frames (out of 50) Emission Angles (out of 9)
A 2 d = 2.5, M = 7, 10 Gordon 50 9
B 2 d = 4.5, M = 7, 10 Gordon 50 1
C 2 d = 6.5, M = 7, 10 Gordon 50 0
D 2 d = 2.5, M = 7, 15 Stampede 50 6
E 2 d = 4.5, M = 7, 15 Stampede/BlueStreak 50 3
F 2 d = 6.5, M = 7, 15 Stampede/Comet 50 8
G 3 d = 2.5, a = 30 BlueHive 50 9
H 3 d = 2.5, a = 60 BlueHive 50 9
I 3 d = 2.5, a = 90 BlueHive 50 9
J 3 d = 4.5, a = 30 BlueStreak 50 9
K 3 d = 4.5, a = 60 BlueStreak 50 9
L 3 d = 4.5, a = 90 BlueStreak 50 9
M 10 BlueStreak 50 9


Individual Runs

A

B

C

D

No image "D_r0_emiss.gif" attached to MachStems

No image "D_r45_emiss.gif" attached to MachStems

No image "D_r90_emiss.gif" attached to MachStems

E

No image "E_r0_emiss.gif" attached to MachStems

No image "E_r45_emiss.gif" attached to MachStems

No image "E_r90_emiss.gif" attached to MachStems

F

No image "F_r0_emiss.gif" attached to MachStems

No image "F_r45_emiss.gif" attached to MachStems

No image "F_r90_emiss.gif" attached to MachStems

G

H

I

J

K

L

M


Separation Comparisons

A/B/C

D/E/F

G/J

No image "GJ_i0_r0_emiss.gif" attached to MachStems

No image "GJ_i30_r0_emiss.gif" attached to MachStems

No image "GJ_i60_r0_emiss.gif" attached to MachStems

H/K

No image "HK_i0_r0_emiss.gif" attached to MachStems

No image "HK_i30_r0_emiss.gif" attached to MachStems

No image "HK_i60_r0_emiss.gif" attached to MachStems

I/L


Orientation Comparisons

G/H/I

No image "GHI_i0_r0_emiss.gif" attached to MachStems

No image "GHI_i30_r0_emiss.gif" attached to MachStems

No image "GHI_i60_r0_emiss.gif" attached to MachStems

J/K/L

No image "JKL_i0_r0_emiss.gif" attached to MachStems

No image "JKL_i30_r0_emiss.gif" attached to MachStems

No image "JKL_i60_r0_emiss.gif" attached to MachStems


Velocity Comparisons

A/D

B/E

C/F

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