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

Secondary flow — where it appears

A flow across the main stream, driven when a pressure gradient set by the bulk acts on slower fluid near a wall. It is what gathers tea leaves at the middle of a cup, moves a river's bed to the inside of a bend, and throws the fast core of a coiled pipe towards its outer wall.

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

The current that runs across the river. The transverse velocity through the depth in a bend, beside the downstream velocity that causes it. The surface water is thrown outward and the bed water is driven inward, the two cross at about half the depth, and the whole profile carries no net discharge — which it cannot, because the cross-section has to pass what it is given. What it does carry is the bed load, inward.

The current that runs across the river

The standard channel calculation is one-dimensional, and a river is not. Put a bend in it and the surface tilts by a few centimetres, which is invisible — and a helix forms, a few per cent of the main flow, which decides where the river will be in a hundred years.

applied · Open-channel The friction a coil adds is one curve in one number, and it is near a square root at large Dean number. Friction over a straight pipe's, at the same flow, against De = Re √(a/R): 1.01, 1.13, 1.4, 1.79, 2.36 at De = 11.6, 30, 70, 150, 300, beside White's fit to measurements and a large-Dean boundary-layer law. Below about 11.6 the ratio is one within a per cent.

A coil's friction is one number, and the coil holds its flow laminar

Bend a pipe into a loose coil and the flow inside is not the same flow bent. The fast core is thrown outward, slow fluid returns round the walls, and a pair of counter-rotating cells appears, about a tenth of the mean speed in an ordinary coil. Dean showed in 1927 that one number governs all of it: Reynolds times the square root of the tightness. Below about 12 nothing changes. Above it the friction rises by a curve the coil's geometry never enters again. And the same secondary flow does something unexpected to transition. A coil stays laminar at four or five times the Reynolds number that breaks a straight pipe.

applied · Internal flow

Named alongside it

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

Model limitBoundary layerConservationCurvatureDean numberDimensionlessFree surfaceFriction factorMeasurementOpen-channelPoiseuille flowSediment

All concepts