Generator

A circle of fluid, 0.90 of a gradient time later

A circle of fluid, 0.90 of a gradient time later
A circle of fluid, 0.90 of a gradient time laterA material circle in a uniform velocity gradient, carried by the exact matrix exponential of that gradient. It becomes an ellipse — always an ellipse, for every gradient — and the axes it stretches along are the eigenvectors of the symmetric half. In an incompressible flow the area is unchanged however extreme the distortion, which is the statement that stretching in one direction is squashing in the other.the circle it started assimple shearu = (y, 0)divergence 0.0000vorticity -1.0000stretch rate 0.5000squash rate -0.5000axis ratio 2.18163area × 1.00000000exp(t·tr L) = 1.00000000a uniform velocity gradient, integrated exactly by the matrix exponentialany Reynolds number — the split is kinematics, with no fluid property in it

A material circle in a uniform velocity gradient, carried by the exact matrix exponential of that gradient. It becomes an ellipse — always an ellipse, for every gradient — and the axes it stretches along are the eigenvectors of the symmetric half. In an incompressible flow the area is unchanged however extreme the distortion, which is the statement that stretching in one direction is squashing in the other.

2 essays call parcel-split. 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 parcel-split 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.

The whole library · All essays