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

Probability — where it appears

A measure over an ensemble of outcomes, used in fluid mechanics to describe a flow whose equations contain no random term at all. What is random is the initial condition and the ensemble rather than the dynamics, and the statistics are a property of that choice.

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

Two lifetimes, crossing. The mean time for a turbulent puff to decay and the mean time for it to split into two, against Reynolds number, on a logarithmic axis spanning thirty orders of magnitude. Below the crossing puffs die faster than they multiply; above it they multiply faster than they die, and the flow stays turbulent.

A puff that does not know how old it is

A patch of turbulence in a pipe below the critical Reynolds number dies at random, and its chance of dying in the next second does not depend on how long it has already lasted. The flow that contains it has a memory anyway, because the patches multiply — and where multiplying overtakes dying is a Reynolds number.

turbulence · Transition How far apart two points can be and still be correlated. The correlation between the logarithm of the dissipation at two points, against how far apart they are in units of the smallest scale, over four decades. It falls as a ratio of logarithms — so it is still a quarter at a thousand smallest scales, and reaches a half only at a hundred.

A dissipation correlated across every scale

The dissipation is supposed to be the most local quantity in turbulence — a thing happening at the smallest eddies, everywhere and independently. A multiplicative cascade makes its logarithm correlated over a distance that is a ratio of logarithms, so two points a thousand smallest scales apart still agree a quarter of the time.

turbulence · Intermittency

Named alongside it

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

IntermittencyMeasurementMemory kernelModel validityRegimeCascadeCorrelationCritical pointDissipationPipe flowRelaxation timeReynolds number

All concepts