Sunday, February 12, 2006

Column 6: Vorticity (originally posted September 29, 2005) (column 5 is outdated, so I won't post it)

Vorticity is one of the major atmospheric properties that's indirectly measured.

In a technical sense, there are many definitions of vorticity, and a couple of types. I'll deal with the definitions first.

Vorticity can be defined as the amount of spin in the air. Mathematically it can be said to be twice the angular velocity of the fluid being measured (our fluid of interest being air) if the fluid is not undergoing any deformation. There's another mathematical definition, but it's really convoluted and I'd lose you all if I wrote it here.

Now, there are also 2 (really 3, but I'll get to that in a bit) types of vorticity. The first type of vorticity is planetary vorticity, which is spin felt near the earth's surface because of the rotation of the earth. It is simply a function of your distance from the equator. Here's a good fleshing-out with a couple of diagrams.

The second type of vorticity is the kind that meteorologists pay attention to. It's called relative vorticity. It's the amount of local spin of an air parcel. There are 2 ways to acquire relative vorticity. The first is by shear. Picture it: (I feel like Sophia from Golden Girls) You're in a balloon high in the atmosphere and you drop a stick. Assuming the stick has very little mass, it'll be strongly influenced by the winds around it. Now suppose that the winds beneath you do something interesting and pretty impossible: the winds are all from the west, but to your north the winds are 50 km/h and to your south the winds are 150 km/h. And it just so happens that the interface where the winds change is right beneath you, right where you dropped this nearly-massless stick. The north half of the stick is hit by the winds of 50 km/h and the south half of the stick is hit by the 150 km/h winds. What do you suppose happens to the stick? It starts rotating counterclockwise (as you look down upon it), does it not? The stick, due to the shear, has acquired relative vorticity. The other way to get relative vorticity is related to the first--when you have curvature in a flow, air parcels tend to accelerate if they're going around a curve, creating shear vorticity, too. Here's a good explanation of relative vorticity.

Add the planetary and relative vorticity together, and you get (the 3rd type), absolute vorticity. That's what's forecast and indirectly measured on most weather charts (usually at 500 mb).

Now, there's a good reason we measure vorticity.

Again I won't go into the mathematical treatment of this, as it is very mathematical and theoretical, but it works. Essentially, positive vorticity advection induces upward motion. And I'll give an explanation as to why.

Picture a parcel of air moving through the flow, about to encounter a trough. Now I will quote Chuck Doswell because he's more eloquent at explaining such things than I am.

"The trough, in a very real sense, is defined as the blob of enhanced vorticity. Now, consider a parcel entering the trough from behind [moving from west, into the trough, to the east]. This parcel has some vorticity value as it enters the trough. Along its trajectory, it is encountering more and more cyclonic vorticity values. If it is to stay in equilibrium with its environment, it must increase its vorticity. How can it do so? For purposes of this non-technical discussion, I will use a "sort-of" equation: the only way an air parcel can increase its vorticity is to do what ice skaters do to increase theirs: the air must converge, so that conservation of angular momentum requires the spin to increase. By this reasoning, parcels entering the backside of the trough, in a region of anticyclonic vorticity advection (AVA) (that is, vorticity values are becoming more cyclonic along the flow) are having to converge. By the same argument, in the region of cyclonic vorticity advection (CVA) on the other side of the trough axis, parcels are diverging."

Now this is all assumed to happen above the level of non-divergence (LND), where the following happens: if you have convergence at this level, you get a surplus of air. This surplus tries to move up but slams into the seemingly impenetrable barrier of the tropopause, so it must move downward. Conversely, if there's divergence aloft, this implies a lack of air. Air from below moves upward to replace it. So essentially when vorticity is increasing, it induces upward motion (lift) and when vorticity decreases, it induces downward motion (subsidence).

I'm sure you can infer all the implications of this: large-scale (synoptic) storms as well as small-scale thunderstorms are influenced by this. Vorticity increase helps produce clouds and precipitation.

So how do we identify (positive) vorticity (also known as a "vorticity maximum" or "vort max")?

Well, my favourite way of identifying it is by satellite imagery, usually the water vapour images. It's easy to find vorticity centres--I just look for the swirlies. As the swirlie approaches, you can bet that the air is rising. As the swirlie retreats, the air is likely subsiding. Another way to find vorticity centres is on upper air charts; as Chuck metioned before, troughs imply increased vorticity. In fact, sometimes an upper trough will cut off from the main flow and become an upper low, or an upper vorticity centre. Or sometimes you'll see an upper trough on the water vapour image and it'll have a bunch of embedded swirlies in it.

All in all, vorticity is a very important, often-used term in meteorology. When I first heard it, I was intimidated. But now you'll hear me talking about "vort centres" with the best of them.


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