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Analysis of Possible Issues
The Formation of the Axial Wiggles and Slow Knots
Here's a frame-by-frame study of the early evolution of the spherical wind model with Rjet=0.5. This particular model is an extreme case of rapid knot formation so it's worth a look. Density is on the left (red is highest) and temperature on the right (light cyan is the coolest, orange is hottest, black is 10,000K).
Follow the "nascent puncture" (pink arrows) starting at 24y.I believe that the puncture is the underlying problem that we face. Then follow the slow knot/jet that forms next to the axis (purple arrows). Note how the pixelated early frames portend what will happen to the thin and dense swept-up rim a little later.
Follow the knot. If forms at 71y while the rim is still moving slowly. At later times the speed of the rim increases, leaving the knot behind. Then at about 140y the stellar wind slams into the knot creating a poorly resolved ablation flow with a tail that points upward.
My interpretation: The hot gas inside the advancing puncture zone burrows and pushes into the rim laterally. This pressure forces the axial knot to become denser and thinner. (Another smaller knot to its left also forms inside the rim). That is, thermal pressure in the puncture zone is the proximate cause of the wiggles along the rim. If I'm right then controlling the temperature of the early wind is the key to suppressing the wiggles.
Finally, ask whether there is something simple that we could impose on the early flow to suppress the formation of the puncture region. For example, could we force the wind to have the specified density njet and temperature tjet in a thin annular zone of pixels adjacent to and outside of the launch surface?
Report on the Launch Pixelation — Slow Axial Knot/Jet Issue
This is a short followup to the previous section in which I stacked a series of 9 early frames from the output of a spherical run in which namb=4e2, njet=4e4, vjet=200, and Rjet=0.5. In order see how the early growth of the spherical model evolves if the pixelated launch sphere isn't flat across its top (near the y axis) I ran an identical sim except that Rjet=0.55.
The results of the Rjet=0.50 and Rjet=0.55 runs are in the figure below. Look first at the final frame, t=188. What had been a divot in the flow at the y axis has turned into a jet. Then look at the panels at which t=0 in order to see how the pixelated shapes of the two models compare.
I emphasize that R~0.5 is a worst case" since the pixelation of the launch sphere is rather severe. As we saw a few days ago, spherical flows like these but with Rjet-1 and Rjet=2 gave much better results. However, as I'll show next, increasing Rjet doesn't help some other more collimated flow geometries. You'll see that huge artifacts develop along the y axis no matter what the value of Rjet. For them we really must launch the flow at around 45 deg or else find a way to fix the pixelation-related issues near the launch zone.
Astrobear's Outcomes and Its Initial Conditions
At rkemmerer/Significance of R_jet these figures are posted. They show how the outcomes of spherical flows into an AGB wind of namb=4e4 depend on Rjet.
I emphasized how much Rjet matters to model outcomes, and how users of Astrobear must be very circumspect about how the pick Rjet. We found that Rjet=1 is a reasonable compromise for the spherical wind case.
Here's another related comparison of model outcomes as a function of Rjet.
The images above have identical initial conditions except that Rjet=0.5 (left) and Rjet-2 (right). Note how sensitive the outcomes are to the choice of Rjet.
Comment: note that all of the structure above y=3 (left) and y=4.2 (right) is totally artificial.
We need to invest some thought into how the initial conditions are set by the user and how the user can assure that the outcomes are for the right model. There are a variety of issues here:
- The larger Rjet the more of the ambient background actually changes.
- the launch sphere covers more of the inner structure of the background the the flow never encounters
- although njet is the same all along the launch surface, the ambient density (which falls off with radius) at the edge of the launch zone is decreased (in this case by a factor of 16). This drastically changes the density contrast along the launch surface.
- the mass flux in the flow that enters the grid is increased by the ratio of launch sizes
- the mass in the external environment is that which isn't covered by the launch zone. This may or may not matter,
We need to think about several issues.
- Isn't it somewhat misleading if the effective namb changes with Rjet? That is, shouldn't the initial background be constructed so that namb applies at Rjet and not some fixed point deep inside the launch zone?
- Shouldn't Astrobear compute the total mass (solar units) on the grid at each time step and report the result in std.out?
- Should the user be able to specify the total mass injection rate (solar units) rather than njet? That is, one normally knows what
M^dotand vjet are from observations, so njet would be calculated fromrho_jet(r=Rjet) - M^dot/[4 pi vjet (flow area)](3 dimensions)rho_jet(r=Rjet) - M^dot/[2 pi vjet (flow length)](2 dimensions)
where flow area is the area of the launch sphere through which the collimated flow emerges (3 dimensions) or flow length is the length of the launch circle through which the collimated flow emerges (2 dimensions)
- Should there be a writeup for novice users that explains exactly what namb means and how Rjet can affects the outcome?
My Interpretation of the Formation of Axial Knots
The purpose of the figure is to explore how the axial structures in the 212-y outcome (right panel) can be explained.
Each panel is a closeup of the first few frames of a sim of a spherical wind (400cm-3) into an AGB wind (4e4cm-3) with Rjet=0.5. Time markers and scales are shown. The frame to the far right is the outcome after 212 years (this image has a scale change by x2). The main features of the outcome frame are a pair of dense knots — one on the axis and another one to its left — and a tongue of higher-speed, low density gas between them.
Look at the row of pixels right immediately above above the solid green areas in frames 2, 3, and 4. (I stress that you should be looking at rows of adjacent pixels just ahead of the dark green zone.) In each of these rows note how the density colors change from light shades towards the axis to denser shades to the left. That portrays a lateral density gradient. Its pretty strong (almost a factor of 10 over 4 or 5 pixels). You'll see similar gradients in the rows all along the green launch sphere. In a perfect universe the density gradients shouldn't be there. They're artifacts.
These density gradients induce lateral velocity gradients away from the symmetry axis, as you can easily see in the right panel (darker is faster). That is, find any lateral density gradient in any of the left panels. Then look at the corresponding pixels in the same row of the right panels. Wherever there's a density gradient on the left side there's a pretty snappy and corresponding velocity gradient pushing gas away from the y axis on the right side. In a perfect universe the velocity gradients shouldn't be there either.
Look at the fourth panel where I identify both an upward and a lateral thrust. You'll see corresponding features in the other frames too. The lateral thrust (comprised of hot gas) compresses the gas in the rim to its left and to the right thereby forming rapidly cooling dense knots on both sides. This is how the knots arise and increase their densities. The upward thrust produces a tongue of hot gas that races ahead of the knots. This thermal-pressure-driven tongue rises upwards for the rest of the simulation.
Now look at the outcome frame to the far right. By this time the artifacts near the y axis are very well formed. The ram pressure of the wind from below pushes and pushes. The winds strike the knots where ablation-like flows form whose tails point downstream. The protruding tongue of gas will continue to race ahead of the knots, now driven by ram pressure. At even later times the tongues eventually open up and try to envelop/surround the knots. See the second image below at 377 y where gas temperature (not speed) is shown on the right side.
So the development artificial slow axial knots is not that difficult to follow. The process begins with some very small-scale density gradients just ahead of the out-flowing winds at early times and continues onward. The real issue is why those micro-gradients form at early times and how to suppress them. BTW the artificial structures are not the direct result of vortices from sheared flows near the y axis. But once the slow knots form we can expect vortices and stagnation pockets to develop downstream. Of course they are the effects, not causes, of the knots.
Finally, I suspect that in sims where the spherical winds rising upward near the y axis are very dense (roughly as dense as the knots), then their ram pressure blasts away these knots before they have an opportunity to take root. We rarely see artifacts in sims like these and they never become a pest. So there's no doubt about all of the evolving structures in those models.
Shapes and Launch Variations
All images: various tapered flows (all with width=15 deg, vjet=200) into AGB winds (no torus) in which namb/njet = 100 (sparse winds). This general configuration has been particularly susceptible to artificial structures appearing along the y axis. Note that the distance traversed by the flows in 500y increases strongly with Rjet. That's because the rate of mass ejection and momentum flux scales with the area of the orifice, so flows from wider orifices have more uuumph and drive forward further. They also don't encounter as much dense ambient gas for the first 100 years (that is, Namb( r) is the same in all models.) The structures at t=94, 309, and 495 years are over plotted.
Top row: This is the standard set of parameters that I've been using: njet=400, namb=4e4, and various Rjet. The artificial structures appear early in the flow and then increasing poison the rest of the lobe. Obviously Rjet=0.5 is the worst case. However Rjet=2 is badly afflicted after 500 years. I would have trouble deciding what the shape of the lobe really is in every case.
Middle row: Identical to the top row except that the flow is launched diagonally. The axial problems disappear. The shapes of the sims for Rjet=1 and Rjet=2 agree very nicely. There's some flattening of the flow's leading edge for Rjet=0.5. Bear in mind that the momentum flow in this sim is a good bit less than the other sims, and unlike the other two cases in this set, the flow must climb through some very dense AGB winds for the first 100 years.
Bottom row: Identical to the top row except that Njet=4e4 and namb=4e6 (their ratio is still 100). I had speculated that higher density flows tended to overwhelm and partially suppress the artificial axial knots and jet. This seems to be the case.
