Vorticity help

[Nick Bender]

Quick question I came across in my studies this evening.

Streamwise vorticity is the amount of horizontal vorticity that is parallel to the storm inflow. Storm inflow is simple enough, it's the velocity of the low level wind flowing into a thunderstorm. i.e. 15 m/s out of the southeast (not sure if this value needs a direction.) Horizontal vorticity is vorticity generated by a change in wind direction with height - se wind 850mb, w wind 500mb, or wind speed with height - 10 knots 850 mb, 65 knots 500 mb.

Question, how do I calculate a value for streamwise vorticity from a operational forecasting point of view? Wouldn't one first have to calculate horizontal vorticity, before calculating how much of it is parallel to the storm inflow - which would be another calculation. Sounds like either a hodograph operation, or there is already a model that displays streamwise vorticity.

Thanks

 

[Jeff Snyder]

Quick question I came across in my studies this evening.

Streamwise vorticity is the amount of horizontal vorticity that is parallel to the storm inflow. Storm inflow is simple enough, it's the velocity of the low level wind flowing into a thunderstorm. i.e. 15 m/s out of the southeast (not sure if this value needs a direction.) Horizontal vorticity is vorticity generated by a change in wind direction with height - se wind 850mb, w wind 500mb, or wind speed with height - 10 knots 850 mb, 65 knots 500 mb.

Question, how do I calculate a value for streamwise vorticity from a operational forecasting point of view? Wouldn't one first have to calculate horizontal vorticity, before calculating how much of it is parallel to the storm inflow - which would be another calculation. Sounds like either a hodograph operation, or there is already a model that displays streamwise vorticity.

Thanks

As you noted, streamwise vorticity is that component of horizontal vorticity (which, necessarily, is perpendicular to the local vertical shear vector) parallel to the storm-relative wind vector. FWIW, cross-wise vorticity is that component of hortizontal vorticity perpendicular to storm-relative wind vector. This is probably easiest to see on a hodograph... Remember, again, that the local vertical shear vector is tangent to the hodograph, and the local vorticity vector perpendicular and to the left of the shear vector. The basis behind calculating streamwise vorticity in convective storm situations is that there is a correlation between the vertical velocity field and the vertical vorticity field (vertical vorticity is generated by the tilting of the environmental horizontal vorticity, and it is amplified by the vertical stretching beneath the level of maximum upward velocity). We really should talk about the vertical displacement field, which can be quite different (in magnitude and location of max) from the vertical velocity field as well, but this is the gist...

Think about a hodograph that is a half-circle about the origin, with storm motion stationary. In this case, the storm-relative wind vector is always parallel to the local vorticity vector; this hodograph has only streamwise vorticity. Conversely, consider a straight-line hodograph, with a storm motion along that hodograph. Here, the storm-relative wind vector at any particular level is always perpendicular to the local vorticity vector (i.e it is always parallel or antiparallel to the local shear vector); this hodograph has only cross-wise vorticity. Interestingly, consider what happens if a supercell in that straight-line hodograph environment splits... The right-deviating storm (presumably, the cyclonic supercell in the NH) will then have a storm motion that lies to the right of the hodograph, which creates streamwise vorticity.

As a proxy for streamwise vorticity, just use storm-relative helicity! SRH is the area swept out of the hodograph bounded by the storm motion vector. For example, here's a hodograpm from OUN on the evening of 4-24-06, near the time a couple of tornado supercells were ongoing west and southwest of OKC:

The red lines are storm-relative wind 'vectors', and the green arrows indicate the direction of the local vorticity vectors. The entire area bounded by the black hodograph, the left-most storm-relative wind vector, and the right-most storm-relative wind vector (which is near 3km above ground level), is the storm-relative helicity. The storm-relative wind vectors for a different storm motion area given in blue... Note that there is more streamwise vorticity associated with the slower storm motion (i.e. the red storm-relative wind vectors are more parallel to the green vorticity vectors) in the 905-767mb layer, though there is more streamwise vorticity associated with the faster storm motion in the sfc-905mb layer.

 

[Nick Bender]

After reading through it a couple times Jeff I have a better handle on the terminology and its applications than I did before - bravo. Obviously then, the wider an area swept out by the storm-relative wind vectors, the larger values of SRH.

I understand that storm motion can either increase, or decrease SRH, but why? The red lines in your hodograph figure are storm-relative wind 'vectors' for the storm moving east at 2 m/s. Am I correct in stating that at the surface the winds are blowing out of the southeast at ~ 8 m/s, and at 874 mb blowing out of the south at ~ 12 m/s relative to the motion of the storm?

Then storm motion increasing/decreasing SRH would be dependent on the 'shape' of the hodograph. If the 'red' storm would change direction, keeping all other values constant, and move due south at 15 m/s, would it be correct in saying its SRH would increase?

One final question, which storm outlined on your hodograph figure produced? One storm has more streamwise vorticity in the lowest levels of the storm environment, the other has more streamwise vorticity in the lower-mid levels. Which storm would you favor?

 

[Patrick Marsh]

It was the slower movement.

 

[Jeff Snyder]

I understand that storm motion can either increase, or decrease SRH, but why? The red lines in your hodograph figure are storm-relative wind 'vectors' for the storm moving east at 2 m/s. Am I correct in stating that at the surface the winds are blowing out of the southeast at ~ 8 m/s, and at 874 mb blowing out of the south at ~ 12 m/s relative to the motion of the storm?

Yes, that's correct.

Then storm motion increasing/decreasing SRH would be dependent on the 'shape' of the hodograph. If the 'red' storm would change direction, keeping all other values constant, and move due south at 15 m/s, would it be correct in saying its SRH would increase?

Yes, the area swept out by the hodograph and bounded by the storm-relative wind vectors (i.e. the Storm-Relative Helicity) would increase if the storm motion were to be more southerly in this case. It's extremely important to remember that the effect of storm motion on SRH depends upon the shape and 'location' of the hodograph. For example, below is a hodograph for which a stationary storm motion yields significantly LESS SRH than a 12-13 m/s storm motion to the east-northeast. Note that the red area is greater than the blue area; SRH for the ENE @ 12m/s storm motion is significant greater than the SRH for the stationary motion.

Oftentimes, the longer the hodograph, the greater a change in SRH that results from a change in storm motion (mainly the component of storm motion perpendicular to the hodograph, since that "moves" the storm motion vector farther from the hodograph, increasing storm-relative winds and SRH). The gist is that you want to get the storm motion the farthest away from the hodograph as you can (which results in stronger storm-relative winds progressively less perpendicular to the local vorticity vector / progressively less parallel to the shear vector).

One final question, which storm outlined on your hodograph figure produced? One storm has more streamwise vorticity in the lowest levels of the storm environment, the other has more streamwise vorticity in the lower-mid levels. Which storm would you favor?

In the hodograph I posted in a previous post, the easterly storm motion does show more/stronger streamwise vorticity from the sfc to ~900mb, but the vorticity above that is almost entirely crosswise. The nearly stationary motion, however, has more streamwise vorticity through a larger depth of the low-levels (particularly from 800-900mb). In this particular case, though the near-surface shear/vorticity is very important, I'd probably prefer the motion that would yield less crosswise vort / more streamwise vort through a greater depth of the low-levels. FWIW, the only two supercells that produced tornadoes that day showed a drastically reduced storm motion near and during the time that they were producing tornadoes. I don't think that was coincidental.

 

[Paul Knightley]

Very useful info, Jeff - thanks. To me this highlights the fact that modelled SREH is to be taken with quite a pinch of salt, as highly deviant storm motions can vastly increase SREH. I remember reading somewhere that proximity soundings in the inflow notch of supercells has shown massive 0-1km SREH.

 

[Nick Bender]

Thanks for the thorough explanation Jeff, naturally it will take a little time using this operationally. Also, good point Paul, along the same lines as how using corrected virtual temperature on a skew-t can drastically increase CAPE values.

So Jeff, the tornadic supercells 25 April 2005 showed drastically reduced storm motion near and during the time they produced tornadoes? Wouldn't this mean, given the 00z hodograph, the storms increased their streamwise vorticity through a relatively larger depth compared to the streamwise vorticity being produced prior to the reduced storm motion?

I could be grasping at straws trying to make the conncetion with that case, as I imagine the storm motion increasing/decreasing streamwise vorticity/SRH is really dependent on the size/shape of the hodograph.

[logic check]
By running up streamwise vorticity values, in essence you are also running up SRH values. It's obvious then why long, curved hodographs are favorable for intense, rotating updrafts. However, straight-lined hodographs aren't necessarily unfavorable even if the storm motion parallels the hodograph. While you do have pure cross-wise vorticity, if there is a good amount of speed sheer which could be turned into the vertical, I imagine you would be in business then as well - though straight-lined hodographs favor splitting storms, no?

 

[Jeff Snyder]

Thanks for the thorough explanation Jeff, naturally it will take a little time using this operationally. Also, good point Paul, along the same lines as how using corrected virtual temperature on a skew-t can drastically increase CAPE values.

Yes, Paul does bring up a good point re: model SRH. Some hodograph shapes/sizes are extraordinarily sensitive to minor changes in storm motion, so it's very important to realize the model forecast storm motion whenever you look at model forecast SRH! If storm deviate from what the forecast indicated, there could be substantially enhanced (or reduced!) SRH. Note that this also means that two storms in the exact same environment but with different storm motions will likely "ingest" different SRH.

So Jeff, the tornadic supercells 25 April 2005 showed drastically reduced storm motion near and during the time they produced tornadoes? Wouldn't this mean, given the 00z hodograph, the storms increased their streamwise vorticity through a relatively larger depth compared to the streamwise vorticity being produced prior to the reduced storm motion?

That sounds like a legit hypothesis.

I could be grasping at straws trying to make the conncetion with that case, as I imagine the storm motion increasing/decreasing streamwise vorticity/SRH is really dependent on the size/shape of the hodograph.

[logic check]
By running up streamwise vorticity values, in essence you are also running up SRH values. It's obvious then why long, curved hodographs are favorable for intense, rotating updrafts. However, straight-lined hodographs aren't necessarily unfavorable even if the storm motion parallels the hodograph. While you do have pure cross-wise vorticity, if there is a good amount of speed sheer which could be turned into the vertical, I imagine you would be in business then as well - though straight-lined hodographs favor splitting storms, no?

When you look at hodographs, you don't really need discriminate between "speed shear" and "directional shear". Indeed, both "components" of shear jointly affect the shape and 'size' of the hodograph. The idea of streamwise vorticity is that there is tilting (and stretching, where applicable) of horizontal vorticity (generated by vertical wind shear) within the updraft (or nearly within the updraft -- vertical vorticity max doesn't necessarily need to be colocated with the vertical motion max). With crosswise vorticity, the location of the vertical motion max/min are rotated 90 degrees from the location of the vert. vorticity max/min (i.e. the vertical motion field is uncorrelated with the vertical vorticity field). So, as long as the storm motion vector lies on a straight-line hodograph, there is only pure cross-wise vorticity. Now, internal dynamics within a storm can cause it to split, which in turn can lead to a new storm motion that is off the hodograph. This, consequently, yields streamwise vorticity (and SRH).

 

[Nick Bender]

Case closed.

Thank you very much guys.