Quick question on horizontal vorticity

[Nick Nolte]

I've been going through the educational modules on meted and in the Principles of Convection III: Shear and Convective Storms, there are diagrams (including one using a paddlewheel as a visualization) showing the idea behind vorticity. It talks about positive and negative vorticity, and in the second slide of the cold pool interactions, I just want to make sure I get it.

Is the vorticity from shear there positive because it increases with height? If, for whatever reason, the shear profile was reversed to decrease with height would the vorticity then become negative causing the greater lift to be on the left side of the cold pool in that graphic?

 

[Greg Blumberg]

This is awesome because I actually have an exam on this stuff today!

You get positive (cyclonic/counter-clockwise) horizontal vorticity because your wind speeds increase with height (or your typical wind shear.) If you flipped the winds around (which is impossible) so the fastest wind speeds were at the surface and your wind speed decreased with height, you'd get negative (anti-cyclonic/clockwise) horizontal vorticity.

Cold pool interactions have to do with the creation of vorticity from density differences between the air masses. This is typically referred to as the baroclinic vorticity generation. A good metaphor is to ask yourself...what happens when you kick two soccer balls with the same force, but one soccer ball is heavier (and much more dense) than the other? One is able to move further away, thus leading to a "shear" of the soccer balls. Same thing happens with the air masses. I assume this concept applied to cold pools would generate positive (cyclonic/counter-clockwise) horizontal vorticity.

As for lift when it involves horizontal vorticity...I have to admit my knowledge in that area is limited. I haven't seen the graphic you are talking about.

Does this answer your question? When I read the question, it was a little confusing what you were asking for.

 

[Nick Nolte]

yeah, that basically answers my question, thanks. The module talks about the vorticity generated by the interaction of shear and the cold pool and what effects that has on lifting parcels. I realized that wind speed doesn't decrease with height, but asked about that scenario to make sure I understood the model they were presenting.

According to the slide (if my understanding is correct), the upshear side of the cold pool generates positive vorticity, and so does the vertical wind shear. This causes any parcels at that point to be dragged up and over the cold pool, failing to provide the direct lift needed to raise it to the LCL.

Whereas on the downshear side, the cold pool generates negative vorticity while the ambient shear still generates positive vorticity...if these two forces are balanced then parcels are accelerated straight upward, kind of like a baseball going through one of those automatic pitching machines, except pointed straight up in the air.

 

[Greg Blumberg]

That kinda sounds right...could you send me the link to the module online so I could take a look at it?

 

[Jeff Snyder]

You get positive (cyclonic/counter-clockwise) horizontal vorticity because your wind speeds increase with height (or your typical wind shear.) If you flipped the winds around (which is impossible) so the fastest wind speeds were at the surface and your wind speed decreased with height, you'd get negative (anti-cyclonic/clockwise) horizontal vorticity.

Wind speeds increasing with height need not result in positive horizontal vorticity. For example, if we look at a southerly LLJ (which we commonly see in the Plains) characterized by a speed max at 1-2 km above the surface, the horizontal vorticity between the surface and the jet max is in the "negative" x-dir (i.e. a vector pointing to the west). Vorticity is a vector quantity, which means that we need information about the speed AND direction of the flow in order to calculate vorticity. Vorticity is defined as del x U (the 3D wind vector). The horizontal components are given as:

(dw/dy-dv/dz)*i_hat + (du/dz-dw/dx)*j_hat

where i_hat and j_hat are the unit vectors in the x- and y-directions, respectively. If we neglect the contribution of gradients in vertical velocity by assuming a constant (or zero) vertical velocity, then we just have the following:

-dv/dz*i_hat + du/dz*j_hat

Even on a larger scale, wind speeds CAN be maximal in the low-levels and decrease in speed with height -- this is exactly what we see in tropical cyclones for the most part. We can then use the thermal wind relation to explain this general structure of warm-core low-pressure systems. I'm digressing a bit, but wanted to detail horizontal vorticity a bit. We are usually interested in whether the vertical component of vorticity is positive or negative, but that depends upon what you're doing, I suppose.

In terms of the interaction between horizontal vorticity generated as a result of the horizontal gradients in buoyancy through the edge of the cold pool and horizontal vorticity associated with the low-level wind shear, I'll point you to The Shear and Convective Storms module from COMET MetEd (note that you may need to register first, but it's free). I'll also refer interested readers to the Severe Convection II: Mesoscale Convective Systems COMET MetEd module that also discusses the interaction of low-level wind shear with the cold pool in terms of cell (re)generation.

 

[Nick Nolte]

Greg, the slides I'm referring to are in the first link Jeff posted in his last paragraph.

Jeff, those were the modules I was specifically referring to in my initial post. I think I see why, in your example, the vorticity vector would be negative...simply because the wind direction would back with height, yes?

I think that slide in the Shear and Convective Storms module with the paddlewheel metaphor is a 2-D representation, and just describes what would happen with speed shear, it seems to me that it leaves out, or ignores any directional shear, unless I completely missed that part.

I figured I'd wrap my head around that before I go shoving a third dimension in

 

[Greg Blumberg]

Thanks for fixing my mistakes Jeff. I was trying to simplify the concept using a simple linear 2D flow without vectors and it didn't quite go as planned I guess. Hope this isn't what happened on my test! I do know this stuff!

Thanks for posting the link! I'll check that out when I get some time this weekend.