Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Concept

Strain — where it appears

The part of a flow's velocity gradient that stretches fluid elements along one direction and squeezes them along another, without rotating them. It is what pulls a vortex into an ellipse and, past a limit, into filaments.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The flow stops and the stress does not. Shear stress against time for a fluid sheared at a constant rate for two seconds and then left alone. Nothing is moving after the second mark and the fluid is still stressed: 37 per cent of the peak one relaxation time later, and 0.7 per cent after five.

The fluid that has not finished its last deformation

Shear a polymer solution for two seconds and stop. Nothing is moving and the fluid is still stressed — 37 per cent of the peak one relaxation time later, and still measurably stressed after five. Two histories imposing exactly the same total strain leave it in states differing by a factor of 3.7.

viscous · Non-newtonian The ring is drawn off while the core keeps its shape. The edges of a vortex with a core of twice the ring's vorticity out to six-tenths of its radius, at four times, in a strain raised to 0.245 — just past the 0.227 that strips its ring. The strain stretches along the horizontal. Both edges lean into the ellipses of a strained vortex; then the ring's edge is pulled out at its two tips into arms, while the core inside stays close to an ellipse.

A strained vortex loses its ring at the limit of what it holds

A uniform patch of vorticity survives a strain up to 0.150 of its vorticity and no further. A real vortex is not uniform: its vorticity falls off outward, and in a strain its weak outer layers are drawn off while its core survives. The obvious way to predict how much survives is to apply the uniform limit layer by layer, each layer to its own vorticity. It is wrong by up to a factor of three. Built from a core inside a ring and followed by contour dynamics, the ring is stripped not at the limit of its own vorticity but at the limit of all the vorticity inside its edge, and a little after it.

inviscid · Vortex patch

Named alongside it

The objects these essays reach for when they reach for this one.

CirculationContour dynamicsConvolutionDeborah numberFilamentMeasurementMemory kernelModel limitModel validityNon-newtonianPolymerRegime

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