Downburst in a Vortex

[Robert Edmonds]

This weekend I produced an interesting little simulation. I just updated this model (for other purposes) converted it to cylindrical coordinates and added a staggered grid (first time I tried this with my own models). Anyhow, basically put a downburst in a vortex (or a vortex in a downburst).

Anyways... Again, the images are in cylindrical coordinates. That is, going to the right is increasing radius, and going up is simply increasing altitude. I have kept the simulation 2d, so this can be thought of as a cylindrically symmetric 3d simulation. The left panel shows the density perturbation, that is it is correlated to the buoyancy of the air (more red more negative buoyancy). The right panel shows the tangential velocity (in the theta direction). The background environment is (dry) adiabatic.

There are two main surprises. First the dense bubble of air splits (turning into a ring in 3d) before reaching the surface (this doesn't occur if there is no vortex). Second, likely due to the convergence of the ring of dense air hitting the surface, the wind speed actually increases to a factor of ~4/3 the initial velocity, before the vortex largely dissipates. The box size is ~2.5km and the movie essentially plays through several minutes.



I'd be happy to field any questions, I may not know all the answers since I haven't had much time to interpret the results...

Edit:
Adding to this post a simulation from a different run to help in contrasting the differences with and without the vortex. Below is a run (from a different code I made) of a cool bubble in 3d.


Blue in this case is the temperature perturbation, thus why blue not red (in the other simulation it is the density perturbation).

 

[Chip Redmond]

With the first simulation, the left panel with buoyancy, why does the bubble actually move outward with decreasing height? It doesn't fall directly under the origin. Are you assuming shear within the column? Is this in result of the high ahead of a negatively buoyant parcel and coriolis strengthening the pgf in the outward (increased radius) direction? Just a curiosity.

Finally in the last video with temperature perturbation...I would expect to see a more elongated pool with several Kelvin-Helmholtz turbulent eddies instead of just one that weakens with time along the leading edge. I would gather this because shear in the upper levels, just above the downburst will affect it and create more drag on the top (obviously) stretching it an prohibiting to become defined just on the leading edge.

Chip

 

[Robert Edmonds]

With the first simulation, the left panel with buoyancy, why does the bubble actually move outward with decreasing height? It doesn't fall directly under the origin. Are you assuming shear within the column? Is this in result of the high ahead of a negatively buoyant parcel and coriolis strengthening the pgf in the outward (increased radius) direction? Just a curiosity.

This was what was surprising to me too. Haven't figured it out yet... Coriolis is neglected for this size scale, with it only being ~2.5km (i.e. the Rossby #>>1). I plan to look back into this a little more, just finished my oral exams, so that's been keeping me distracted.

Finally in the last video with temperature perturbation...I would expect to see a more elongated pool with several Kelvin-Helmholtz turbulent eddies instead of just one that weakens with time along the leading edge. I would gather this because shear in the upper levels, just above the downburst will affect it and create more drag on the top (obviously) stretching it an prohibiting to become defined just on the leading edge.
Chip

No initial shear in the second video. In a 2d version you do get some Kelvin-Helmholtz turbulent eddies. However, they're much less apparent because the temperature perturbation decreases much more quickly in the 3d version. That is the temperature perturbation decreases as the the ring of cool air spreads out.

I believe this is what you're thinking of...

There's a version I've been working on with terrain following coordinates, you can find a video of a this density current going over a mountain under the same account.

 

[ahaberlie]

If I am understanding the cylindrical coordinates correctly.. it seems as though you have a continuous but decreasing radius of dense air rising within the vortex aloft. Near the surface you have an expanding radius of dense air away from the vortex and a decreasing inner radius of less dense air as the bubble spreads out and "in."

It seems like the external expansion is fairly consistent with your other downdraft models but the near vortex expansion is a lot slower.

I was going to say that it reminded me of arching radar reflectivity... you see with a void near the surface associated with a BWER and it extends aloft.. forgot the technical name for it..

http://www.sky-chaser.com/image/mwcl2010/bdlgra4.jpg

Do you have any simulations with a larger or smaller vortex radius? It seems like this vortex has a radius around .5 km.

I think your reasoning for the sudden 4/3rds increase is a good thought and quite interesting to think about.

Cool stuff.

 

[Robert Edmonds]

Do you have any simulations with a larger or smaller vortex radius? It seems like this vortex has a radius around .5 km.

Not yet but, I plan to make the runs here shortly. I've been checking a few little other issues first. Just wanted to reply really quick, so you don't think I won't get back to your questions...

 

[Chip Redmond]

I had another quick thought...in cylindrical coordinates within a stable environment the momentum surfaces extend out and down as the radius increases. The bubble of negative buoyancy could be following a surface downward perhaps? PGF increases outward with time...

edit: I had an image and now I can't find it...

edit 2: After I think about it, that wouldn't make much sense because with no shear you aren't including momentum surfaces and there wouldn't be a defined initial starting surface for it to even follow... However, you are initializing a pressure perturbation within the atmosphere with a negative buoyant parcel and this in return would create a momentum surface from the PGF across and around the parcel. Once again this would go back to coriolis almost with the enhanced leftward side, but as you said, the scale is way to small.

Chip

 

[Robert Edmonds]

I've been exploring what happens by increasing the radius of the vortex (keeping the max tangential velocity constant). I've increased the vortex width by a factor of 3 (to ~1.5 mile diameter) and the general trend is the same. As the simulation runs, the amount the tangential velocity increases is slightly more, almost to a factor of ~1.5 the initial tangential velocity. The vortex then begins to dissipate afterward, though to a lesser extent (not too surprising since there's more momentum in the initial vortex). The extent the "cool" bubble expands before reaching the surface increases with increasing vortex diameter. I've been thinking of playing around with how I initialize the starting conditions. What I've been doing is keeping the rho(r) fixed, then changing the temperature to decrease the pressure at the center (so that everything is initially in cyclostropic balance). Another way is keeping T(r) fixed but changing rho to decrease the pressure at the center. Playing with this will allow me to see how the initial conditions affect the results.