Artificial knots for outflow models with spherical nozzles

The following is from Bruce's email. Just want to put here and see if any comments/ideas:'

Thin knots seem to arise in many outflow models along the y-axis shortly after the launch of a jet. In brief, I’m convinced that the biggest cause of such knots is the shape of the nozzle’s surface (a sphere). A flat or highly conical nozzle will suppress the knots.

The simplest flow is that of a cylindrical jet at the origin moving into an ambient medium of constant density on a Cartesian grid. In principle, such a flow has no way to deviate from a simple cylindrical flow unless shears (at the edge) or kink instabilities develop (they don’t).

Heavy flows: This is obviously the case if the flow density > ambient density. The flow is simply a telephone pole flying through something like a vacuum.

Light flows: If the flow density < ambient density then the flow will interact strongly with the dense medium through which it pushes. Even so, there is no apriori expectation that a dense, thin knot will develop almost immediately along the y axis. But it does: that’s what I find in the sims using the present version of AstroBEAR. See the attached figure where I move the viewing window at the same speed as the head of the flow.

Notes:

  1. the spatial units in the graph should be multiplied by two if the basic cell size = 500 AU. I had to mess with the scaling factors in VisIt (0.25 instead of 0.5) to get a good display. That is, the basic cell in the figure wiull have dimensions of 250 AU.
  2. I used Nlevel=5 in these sims. Changing it by ± 1 has no effect.

The panels show a light flow of density 102 and speed 200 km/s moving into a uniform ambient medium of density 104. The bottom panel shows the geometry at t=0. You are looking at the nozzle (round) and (unit) flow vectors that will emrge through its surface at t=0+. The vectors are perfectly vertical. The nozzle’s surface isn’t a perfect shpere, but that doesn’t matter much.

The vectors along the inside edges of the gas displaced by the round jet (the “swept-up, compressed rim”) almost immediately start to curve towards the y axis. This is exactly what should happen when the flow strikes the inner edge of the rim of displaced gas obliquely. The flow along the rim starts to converge towards the y axis. This convergence forms an incipient knot in 100 y (the nozzle crossing time). The knot rapidly becomes longer and denser as mass continues to continues to flow into it.

It’s what you will get if you put a squishy ball bearing between the jaws of a closing scissors.

My point is that artifical knots are inevitable using spherical nozzles. The formation of this axial knot can be suppressed if the nozzle were a flat surface or a long and thin cone. The flow from a flat nozzle would displace and sweep up a flat plug (a disc) whose speed decreases as ambient gas is incorporated into it. The only wat to completely avoid any axial knot is to introduce a flow with a sharply conical head, like the nose cone of a rocket.

Baowei knows through bitter experience that forming a flat nozzle is difficult in AstroBEAR. It’s even more difficult to make a nozzle shaped like a nose cone. But you might think about it. (Of course, some axial knots might form after a simple jet starts to break up or become unstable and pinch. Such knots are ‘real’, not artificial.)

Of course, no one has any idea what a nozzle looks like on large sice scales. Zhou’s sims might provide some guidance on this. They look highly conical to me.

This email sounds like its just about details of flow geometries. It’s really more about model outcomes. There’s potentially important science at stake.

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