I read a mathematical analysis of this perhaps 25 years ago...the
basic principle is extracting energy from the curl of the air
velocity.

Curl? I hoped I'd never hear that term again. That is probably why I
couldn't
complete the Electrical Engineering curriculum in college. Maxwell's
equations
for Electricity & Magnetism - first equation, stated in english: Curl
beta = 0.
ED: What's curl?
Math Geek: Oh, that's just the divergence of the gradient.
ED: Ok, I kind of understand gradient, but what's divergence?
Math geek: Long-winded string of uncomprehensible words.

Ed flunks out.

The most interesting conclusion is that if the curl is the only source
of energy (in other words, there is no vertical velocity component to
complicate the issue), the optimum strategy is amazingly simple. Most
of the variables fall right out of the calculation, and the result is:
Circle in a 55-degree bank. Go to the left if the curl direction is
upward, right if it's downward.
Seems that if you have this really high wind velocity above a certain
level
and zero below that, then trying to circle is going to be difficult to
impossible.
If you have one wing stuck below the layer "anchored" in zero wind, and
the
other in the high velocity layer, you're going to get "rolled",
spanwise, across
the sky, and there's nowhere near enough aileron power to stop that.
And, how would you know if the curl is upward or downward? Seems like
if you guess wrong you get thrown at the ground, real hard.

Ed