Doesn't exist, it's trying to simplify and approximate the truth. Flow is 5 dimensional, we assume 2 orthogonal axis of spin, and we call the other stuff secondary flow. Flow is locally structured in 3 dimensions, and translated in another 2. Locally structured in x, y, and z planes, and the other 2 dimensions are borrowed from electromagnetism, divergence and curl. Divergence is basically pressure gradient, and curl is basically vorticity.
Aerodynamicists create formulas and approximations to encapsulate all 5 dimensions of airflow. Prandtl's lifting line theory, Martin Kutta's theories regarding circulation, and the subsequent Kutta-Jukowski theorem. Which is really just a description of flow around a cylinder, with an applied Fourier transformation. As we all know Fourier transformations are 2-d projections of more complex phenomena.
The problem is we are pea-brained, it's difficult for us to see the nested donuts in airflow, and the 5 dimensions they encompass. It's bad enough we can't see the wind, but worse our tools for analyzing it are dependent on butchered approximations.
A while ago I saw a new propeller design, and then it hit me like a ton of bricks.
https://www.youtube.com/watch?v=MNnB_50Z20IThis thing is just ribbons of a torus.
https://i.ytimg.com/vi/px5kZn_hPbU/maxresdefault.jpg![]()
The vortex ring is a torus, a non-destructive interference pattern. The vortex ring encapsulates all 5 dimensions of flow. X,Y,Z planes of symmetry, divergence and curl, all in one.
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