Trying to get a shock physics perspective on the re-orientation of the collision interface. To do so, wanted to understand the types of shocks generated by the oblique MHD colliding flows runs, and the change in fluid variables over these waves. Started by running a 1D tilted infinite Riemann problem, so to speak. It is generated by inflow conditions in X, and has periodic boundaries in Y. The incoming velocity and magnetic field vectors correspond to the 30-degree tilted CF case. Mach = 1.5, and Beta = 1. Cooling and self-gravity are turned off.

Here is density psuedo with velocity vectors and magnetic field streamlines overlaid:

Over the fast wave front, we see the expected bending of the velocity field away from the normal of the shock, and corresponding bending of the field lines. The color bar for the streamline plot measures strength of B, and so we see that the field increases in strength over the first jump. The density increases over this jump. Over the slow-shock jump, the field now bends toward the normal of the shock, and this is because the field is tied to the opposing flow. Over this 2nd jump, the velocity interestingly goes to zero. The density increases further. There appears to be a contact discontinuity at the center of the configuration.

To look at the jump conditions on the velocity more closely, here is a pseudo-color plot of the velocity. First is the vx velocity, then vy, and then vmag.

Now, the psuedo-colors plots are in the original coordinate system, whereas the vector plot has been tilted to look like the colliding flow scenario. The psuedo plots show that over the forward shock, the velocity field becomes completely parallel to the shock front (i.e. the x-component vanishes). This forces vy to go to zero over the slow shock front to maintain symmetry (the flow solutions must be rotationally-invariant).

Jonathan recently identified a way of decomposing the types of shocks in the simulations based on an eigen analysis. With this new code, we are able to see the different types of shocks present in the flow. For the MHD/infinite case, we see there are 5 wave fronts:

Now, for the finite case, we have the following density plot:

and velocity plot:

and wavefront plot:

When the scenario is finite, there is now pressure gradients between the collision refion and the ambient that allow for a radial expulsion of gas from the collision region. Over time in these plots, we see both the reorientation of the inner surface of the collision region, as well as the outer (fast) shock front. Here are 3 likely scenarios for the reorientation of the inner collision region.

More x-momentum due to kinking and shear flow and balance between pressure and radial expansion.
In this picture, the radial expansion of the flow drags the field lines out of the collision region. Depending on which side of the interface you are on, this is either enhanced by the shear, or partially cancelled out. Figure of close up. On the side where the field remains relatively straight, gas doesn't get deflected as strongly as on the other side, given the flow is tied to the field. (Here, could strengthen this argument by better understanding of the connection between field, velocity, in MHD shocks). This leads to more net x momentum on one side of the interface then the other, and thus, torque. A figure shows this to be the case. However, whether this picture for why the momentum gets amplified on one side of the interface is correct, is still unclear.

The radial expansion of gas away from the collision region.
The infinite case teaches us that the velocity goes to zero in the center of the collision region in the MHD case. However, when there is a pressure gradient between the collision region and the surrounding ambient gas, we see a strong outward (relative to the center of the collision region) velocity field arise. That there is now an up/down (relative to the cylindrical axis of the flows) velocity field within the collision region, sends gas upward and downward, thus effectively straightening out the collision region. In the hydro case, this is not the case, as there the velocity field is the usual sheared flow field. (Which, by the way, uh-oh for our runs declaring to study a 'shear' effect). Thus, we do not see a realignment of the interface in the hydro case. In visit, drawing a line along the original collision angle shows supports that the interface realligns in the MHD case, but not in the hydro case.

In the 3rd scenario, it may be due to the tension in the field. (Rubber-band model).
Just a glance at the magnetic field threading the collision region shows suggests this would be a contributing factor.

For the outer wave front (fast shock), the apparent reorientation can be explained by a stalling of this wave front, as seen in the upper right/lower left corners of the collision interface. This is happening because there is a loss of magnetic pressure behind this wave front, and thus, the shock loses its support and stalls (see following figure of magnetic pressure map). The enhanced magnetic pressure, relatively speaking, in the opposite regions are due to the combined effect of 1. the deflection of material and 2. the enhanced pressure from radial expansion. In regions where the magnetic pressure is strongest, the wave front is supported and continues to move outward, thus appearing to straighten the outer wave front.

In the hydro case, we do not see this reorientation (at least in 2D). Instead, we find a staircase effect. This seems to be getting generated by vortices above and below the collision region. Material that is deflected away from the flows by the shear, falls back down onto the cylinder due to pressure gradients. This additional material then creates more x-momentum/ram pressure, which drives the stair-casing structure.

We can imagine writing these results up in a paper, which could have the following components:

1. Simulation results

2. Description of Jonathan's method for picking out types of shocks

3. Types of shocks present in the different cases

4. Predictive formula for reorientation in terms of beta and mach