RKW Theory

[Metsfan]

Can someone chime in on this theory. 

 

When there is a cold pool and no shear (second figure) I thought that the updraft of the storm would lean upshear and back up and over the cold pool weakening the storm, but the rwk theory image shown below says that the updraft leans up and over the cold pool when there is only shear and no cold pool ©. I thought that in figure c that if there was only shear the effect of the shear would tear a storm apart. Thanks for your responses. If it isn't too much can someone explain each figure. :-)

 

[bdgwx]

I am by no means an expert so if someone sees anything wrong with the following then please let me know so that I can learn as well.
 
First, here is a paper that has better diagrams and explains them better as well.
 
The storms are moving from left to right in an environment with mean wind vectors all pointing to the right as well. I find the arrows to the right of the figures ( b ) and ( d ) to be somewhat confusing. I think it would have made more sense to point the arrow in the direction of the ground-relative wind. Instead, they point in the direction of the storm-relative wind. I do see why they did it that way though.
 
So the arrows, in ground-relative form, would look like the following where U is upshear and D is downshear.
 
( a ) & ( b )
 
U ----------> D
U ----------> D
U ----------> D
 
( c ) & ( d )
 
U ----------> D
U ------>     D
U -->         D
 
Then by using the right hand rule the "-" sign represents vorticity that is pointing out of the diagram (away from the monitor) and the "+" sign represents vorticity that is pointing into the diagram (towards the monitor).
 
Now I always imagine density currents (cold pools) and updrafts using my right hand with palm facing up and fingers pointing in the direction of the storm-relative movement. So a cold pool moving left would have "+" vorticity (thumb point into the monitor) and one moving right would have "-" vorticity (thumb point away from the monitor).
 
Next I imagine vertical wind shear using my right hand with palm facing down and fingers pointing in the direction of the ground-relative mean flow or the downshear side. So winds increasing with height would have "+" vorticity (thumb point into the monitor).
 
Figure ( a ): The updraft on the left side is slanting to the right. Using your right hand with fingers pointing to the right and palm facing up you can see that the thumb is pointing away from the monitor so it creates "-" vorticity on the left side. On the right side everything is the opposite so your thumb is pointing into the monitor so it creates "+" vorticity on the right side. The vorticity couplets are balanced so the updraft stays upright.
 
Figure ( b ): The cold pool is moving to the right and so it creates "-" vorticity. The updraft is moving to the left so it creates "+" vorticity. However, the cold pull circulation dominates in a no-shear environment so the updraft has a tendency to pull up and over the cold pull. Imagine your right hand being the cold pool (palm face up and fingers pointing to the right). When you curl your fingers up they will rotate counter-clockwise. In other words, the vorticity of the cold pool is more than that of the updraft.
 
Figure ( c ): The updraft is moving to the left so it creates "+" vorticity. The cold pool is nonexistent so the updraft circulation dominates with the environment blowing it downshear. The vorticity of the updraft clearly dominates because there is no cold pool.
 
Figure ( d ): The cold pool and updraft circulations are now balanced. A vorticity couplet, "-" from the cold pool and "+" from the updraft, forms and enhances upward vertical motion. Again, using your right hand to model both the cold pool and updraft you can see that when you curl your fingers they point up for both.

[Metsfan]

Thanks for the explanation! The figure that I posted was incorrect as they made a mistake with b and c. Here is the correct one which is what I assumed, and you described. b would lean back over the cold pool and c would be shear dominate so it would tear the updraft storm apart.