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

Stokes' theorem — where it appears

The identity relating the circulation round a loop to the vorticity through any surface spanning it. It is what makes circulation and vorticity two views of one quantity, and it converts a line measurement into an area one.

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

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 The bath is ten thousand times too small. The Rossby number — the ratio of the inertial term to the Coriolis term in the momentum equation — for eight flows at 45 degrees, on a logarithmic axis. Above one, rotation is a correction; below one, it is the physics. A draining bath sits at 3.2e+3 and a mid-latitude depression at 1.9e-1. The Coriolis term is not absent from the bath: it is present, computable, and four orders of magnitude smaller than the terms that decide what happens. Saying so is not the same as saying it is zero.

The bath does not know the hemisphere

The Coriolis term in a draining bath is not absent. It is present, computable, and about four hundred times smaller than what a hand left in the water an hour ago is still doing — which is a ratio rather than an opinion, and it is the same kind of argument as a Reynolds number.

misconceptions · Coriolis scale

Named alongside it

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

CirculationAngular momentumBoundary layerCoriolis parameterDimensionless numberInertial circleIrrotationalKelvin's circulation theoremMisconceptionThe no-slip conditionRossby numberRotating frame

All concepts