DOWNLOAD-DESKTOP-NOTEBOOK.nb (2.5 MB)
6 Likes
Congratulations – you have earned Featured Contributor Badge
Your exceptional post has been selected for our editorial column Staff Picks and Your Profile is now distinguished by a Featured Contributor Badge and is displayed on the Featured Contributor Board. Thank you!
3 Likes
Great article! I thought I’d point out though that looking closely at Fig 1, many of the arrow directions in the outer region (3) and even the middle region (2) look a bit random 
A little bit of AI sloppiness (assuming that’s what that is) is amusingly ironic in this article. But also seriously, I’m guessing regions 2 and 3 rotate the same way as region 1? Do some of the pulses in region 2 really rotate oppositely? Not key details to understanding this article, but good to get them right
2 Likes
Thanks for catching that. I had actually noticed some of those wrong arrow directions while making the figure and tried some prompts to get them corrected, but the image generator kept reintroducing a few wrong arrows. Eventually I lost patience and left it as it was. 
We have now corrected the image.
And yes, your interpretation is right: the main azimuthal flow in all three regions rotates in the same direction. Region 2 does have oscillatory velocity pulses superimposed on this background flow, so locally the velocity can be wavy and can acquire inward/outward components or other small modulations. But the net azimuthal direction remains the same as the background circulation since the scales of the background flow and the pulse amplitude are:
u_{\theta,\mathrm{background}} \sim q^{-1/2-h}
A_{\mathrm{wave}} \sim q^{-1/2-h/2}
h>0 \quad\text{and}\quad q\to 0
3 Likes
Thanks for the correction and elaboration!
1 Like