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

Viscous flow — where it appears

Flow in which the shear stress matters, so that the no-slip condition applies and the equations are of second order across a wall. It differs from inviscid flow in what may be imposed at a boundary as much as in what happens in the interior.

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

Flow past a cylinder at Re 100. A real fluid past a circular cylinder. At low Reynolds number the flow closes up behind the body much as the ideal theory says; as it rises the flow separates and a region of reversed flow appears behind, which is where drag comes from.

The two theories, side by side

The exact solution and the real flow, for the same body in the same stream. One is beautiful and predicts nothing has drag; the other is approximate and has a wake in it. Where they agree and where they part is the whole map of the subject.

viscous · Comparison Stokes' theorem on a solved wake at Re 40. A rectangle drawn in a viscous flow that was solved on a grid. The circulation round its boundary is computed by walking the four sides and adding up the velocity along them; the vorticity inside it is computed by adding up the stored vorticity cell by cell. The two computations share no sample point and the theorem says they must agree.

Circulation is vorticity, added up

One of these two quantities is measured by walking round a loop and one by summing over the area inside it, and a theorem says they are the same number. That reconciles the site's most confusable pair — and explains how a flow with circulation can have no spin in it anywhere.

kinematics · Vorticity

Named alongside it

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

Boundary layerCirculationIdeal flowIrrotationalKelvin's circulation theoremModel validityThe no-slip conditionReynolds numberSeparationStokes' theoremVortexVorticity

All concepts