Generator

A tube stretched to 3.0 times its length

A tube stretched to 3.0 times its length
A tube stretched to 3.0 times its lengthThe same tube of fluid before and after being stretched along its own axis. The volume is unchanged, so the area falls by the stretch ratio; the circulation round it is unchanged, because an inviscid fluid cannot change it; and the vorticity, which is the one divided by the other, rises by exactly the stretch ratio. The skater pulling in their arms is the same theorem told about a solid.beforeafterarea 1, ω 1area 0.333, ω 3.000circulation 1.000000 → 1.000000volume 1.000000 → 1.000000an incompressible vortex tube, stretched — circulation and volume conservedany Reynolds number while the stretching lasts; viscosity enters only at the core

The same tube of fluid before and after being stretched along its own axis. The volume is unchanged, so the area falls by the stretch ratio; the circulation round it is unchanged, because an inviscid fluid cannot change it; and the vorticity, which is the one divided by the other, rises by exactly the stretch ratio. The skater pulling in their arms is the same theorem told about a solid.

3 essays call vortex-stretch. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

It is also the blast radius. Changing vortex-stretch changes every figure listed here at once, and on this site it may change what they assert as well as what they show — which is what has to be rebuilt and looked at before the change is believed.

Where it is called

What each of these essays asks for instead of the defaults is on the regime index, which reads the parameters back out of the finished figures rather than out of the placements.

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