3D MHD Shear Flows

Diameter	40 pc
Mach	1.5
Shear Angles	15, 30, 60 degrees
Density	1 cm-3
Beta	1, 10
Initial B-field orientation	Uniform in x
Cells/Jeans Length	64
Cooling	II curve
Final time	20 Myr
Resolution	48 + 2 ~ 200 cells effective
Box size	62.5 x 75 x 75 pc in x,y,z
Boundary conditions	Outflow-only, and multipole for gravity
Self-gravity	On

Orientation of Collision Interface

Plot showing the direction of the tilted interface:

The interface is tilted about y. This is the Shear 15 case.

Parallel-field case; Beta = 1,10

The field is initialized to be uniformly distributed throughout the cylinder and the ambient medium, oriented along the flow axis.

Evolution of the tilted interface

A slice taken through the center of the box, in the x-z plane, shows that in the strong magnetic field case, the interface tends to realign so that it is vertical:

For production runs, the domain needs to be extended in x so that the sheared interface doesn't reach the boundaries.

Instabilities: Beta = 1 is too strong of a field, as it completely prevents formation of the 3 instabilities relevant to molecular cloud formation; thermal instabilities, kelvin helmoltz waves, and the NTSI are all absent in the strong field case. The NTSI seems to be strongest in the hydro case, and KH seems to increase in strength with increasing shear angle.

Column Density Maps

These column density maps are made by summing the density over all cells through a given dimension, using both the gas and sink components of mass/cell. Recall, the interface is rotated about y (as can be seen in above ​plot). In the 'down the barrel case', the vertical dimension is z, and the horizontal axis is y. The axes are given in the other plots.

Comparison Plots

Down the barrel

Down y

Down z

Individual Cases

Shear 15, Beta = 1

Shear 15, Beta = 10

Shear 15, Hydro

Shear 30, Beta = 1

Shear 30, Beta = 10

Shear 30, Hydro

Shear 60, Beta = 1

Shear 60, Beta = 10

Shear 60, Hydro

A strong ring effect is present in the strong beta cases that isn't in the weaker B field and hydro case.

Peak Densities and Sink Particles

A strong magnetic field leads to more sink particles forming by the end of the simulation compared to the hydro case, but at slightly later times.

A weak field case tends to just delay the formation of sinks, but doesn't seem to enhance the number of sinks that form.

This trend holds for both the Shear 15 and Shear 30 cases.

In contrast, the Shear 60 cases do not make sinks, except for the weak field case that makes 1 by the end of the sim.

Run	Time when sink first appears	Number of sinks by end
Beta1, Shear15	Frame 160/200, t=16 Myr	8
Beta1, Shear30	Frame 173/200, t=17 Myr	7
Beta1, Shear60	No Sinks Form	0
Beta10, Shear15	Frame 184/200, t=18 Myr	5
Beta10, Shear30	Frame 161/200, t=16 Myr	2
Beta10, Shear60	Frame 196/200, t=19.5 Myr	1
Hydro, Shear15	Frame 118/200, t=11 Myr	6
Hydro, Shear30	Frame 146/200, t= 14.5 Myr	3
Hydro, Shear60	No Sinks Form	0

Here is a plot of the peak densities in the grid over time:

Perpendicular-field cases

It was not obvious which field orientation to use for the perpendicular field cases, since the shear angle breaks the symmetry of the cylinder. So to compare the difference, here are 3D low res runs of the Shear 15 case with either a y or z field. These were run with Beta = 1 and Beta = 10.

Beta = 1, y-field

Beta = 10, y-field

Beta = 1, z-field

Beta = 10, z-field

Peak densities and sink particles

Further, peak densities were similar in the transverse cases and both did not form sinks,

B-field Direction	Peak Density at .25, .50, .75, 1	Time first sink formed	No. of sinks by end
x	229, 947, 2383, 4934	15 Myr	8
y	27, 58, 69, 88	-No sinks form-	0
z	22, 51, 50, 58	-No sinks form-	0

Beta = 10

B-field Direction	Peak Density at .25, .50, .75, 1	Time first sink formed	No. of sinks by end
x	598, 1140, 1535, 1487	18 Myr	5
y	83, 210, 255, 225	-No sinks form-	0
z	58, 132, 194, 163	-No sinks form-	0

Issues with the perpendicular case