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

Instability — where it appears

The growth of a small disturbance to a flow that would otherwise persist unchanged. Whether it grows is decided by a parameter crossing a critical value, and what it grows into is decided by the disturbance rather than by the parameter.

Named by 5 essays across 4 fields — each of them below, with the objects they name alongside it.

The Ohnesorge diagram, with the boundaries where they belong. The classical map of jet break-up: the Ohnesorge number against the jet Reynolds number, with the five nozzles placed on it. The three sloping lines are Reitz's transitions in the gas Weber number, and their geometry is computed rather than sketched — a fixed We_g means Oh·Re is fixed, which is a straight line of slope exactly −1 in these coordinates, and the assertion checks that a decade in Reynolds number moves each line by exactly one decade. Where they sit is borrowed; that they are straight and parallel is not. A nozzle below and to the right of the last line atomises.

Where a jet stops being a jet

A tap makes drops a few centimetres down, a garden hose makes a stream that carries, a sprayer makes a mist and a diesel injector makes fog. Same liquid, same mechanism, four regimes — and the number that separates them is not the jet's inertia but the surrounding air's.

regimes · Atomisation One sign change, and both of a stall's surprises follow from it. A lift curve with a peak, and the rolling moment a wing makes against its own roll at the same incidence. Below the peak the slope of the lift curve is positive, the down-going wing makes more lift, and the roll is opposed. Past the peak the slope is negative, the down-going wing makes less, and the roll is reinforced. The stalling angle here is 16.46° and the damping changes sign at 17.07°. Nothing in this picture is a spin yet — a spin needs yaw as well — but the engine that drives one is the crossing of that line.

A roll that feeds itself

A spin is routinely described as a stall that got worse, and it is not a stall at all in the sense of an angle rather than a speed. It is autorotation — a roll that sustains itself because past the peak of the lift curve the down-going wing makes less lift rather than more — and the arithmetic says it begins a little past the stalling angle rather than at it.

misconceptions · Stall speed The structure the sensitivity produces. A detonation front, schematically: a leading shock, an induction zone in which nothing measurable happens, and a reaction zone behind it. The induction zone's length is set by the shock's own strength, and because that dependence is exponential the front is unstable and breaks into cells.

A gas that has not decided to react yet

Behind a detonation's leading shock there is a zone in which nothing measurable happens. Its length is set by the temperature the shock produced, exponentially — a one per cent change in the shock shortens it by fifteen per cent — and that sensitivity is why a detonation front cannot stay flat.

compressible · Detonation 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 Rolls turning side by side, with the fastest downwind water where they sink. The fastest-growing mode at a Langmuir number of 0.13, looking downwind, over two roll spacings of 2.89 decay depths and 4 decay depths down. The closed curves are streamlines of the overturning; the dashed curves are contours of the downwind velocity the rolls carry, positive under the lines where the water sinks. At the surface the cross-wind flow converges onto those lines, which is where floating foam and weed collect as windrows. The amplitude is arbitrary, as in any linear mode.

The drift that turns a current into rolls

A current carrying a Stokes drift feels a force the drift makes out of the current's own vorticity, and under a wind that force is unstable. It turns the surface layer into rolls lined up downwind, with windrows where they sink. The rolls need both the current's shear and the drift's; their growth rate sees only the product; and the split between the two decides which motion gets the energy.

kinematics · Stokes drift

Named alongside it

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

MeasurementRegimeMemory kernelModel limitModel validityAngle of attackAtomisationAutorotationAveragingBifurcationCombustionCorrelation

All concepts