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

Wavenumber — where it appears

The spatial frequency of a disturbance, which is two pi over its wavelength. It is the variable a spectrum is resolved against, and in a flow carrying a range of scales it labels which eddies are being talked about.

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

Three thresholds, and none of them is one. The neutral curves for a layer heated from below, computed by taking the smallest eigenvalue of the marginal-stability operator at each horizontal wavenumber. Every curve diverges at both ends — a cell wider than the layer has to carry heat sideways for ever, a narrower one loses it to conduction — so each has a minimum, and that minimum is the critical Rayleigh number. Two free surfaces give 657.5, one rigid and one free 1100.7, two rigid walls 1707.8. Nothing but the boundary condition differs, and it carries a factor of 2.6.

The threshold the walls decide

A layer heated from below convects at a Rayleigh number of 1707.762, and nothing whatever happens at one. The free–free case has a closed form and the two that do not differ from it by a factor of 2.6 — produced by nothing but what the top and bottom surfaces are permitted to do.

turbulence · Convection The curve that lets in more than one answer. The neutral stability curve: the driving needed to sustain a disturbance of a given wavelength. It has a minimum, so at any driving above the minimum there is a whole band of wavelengths that can grow — and the system has to pick one.

The state a machine was started into

Above the critical driving there is not one flow but a band of them, and a container of a given size can hold several. Which one appears is decided by how the apparatus was brought up to speed, and at twice critical there are eight to choose from.

regimes · Taylor

Named alongside it

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

BifurcationBoundary conditionConvectionConvergenceDimensionlessEigenmodeEigenvalueHysteresisInitial conditionInstabilityLinear stabilityMarginal stability

All concepts