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

Frequency response — where it appears

The magnitude and phase with which a system follows a forcing, as a function of how fast the forcing is. A quasi-steady model asserts that the magnitude is one and the phase is zero, and the phase is usually the half that decides whether something is stable.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

The stress a closure predicts, and the stress there is. The Reynolds-stress anisotropy through a step change in the strain rate, against what an eddy viscosity gives — which is the equilibrium value at every instant. The real stress takes about a turnover to get there, and during that turnover the closure is wrong by up to sixty per cent.

A closure with no memory at all

An eddy viscosity says the Reynolds stress is the mean strain rate times a number, now. The stress it is standing in for takes a turnover to arrive, so the closure is the zero-frequency limit of a response that has a lag in it — and the curve it is the limit of is the same shape as an aerofoil's lift deficiency.

turbulence · Closure A particle is a low-pass filter. The fraction of a fluctuating flow's velocity that a particle follows, and the phase by which it lags, against the Stokes number. At one the particle follows 71 per cent of the motion and lags by 45 degrees — which is the corner frequency of a first-order filter, arrived at from mechanics rather than from electronics.

A particle is a low-pass filter

A seeding particle does not report the flow; it reports the flow through its own transfer function. At a Stokes number of one it follows 71 per cent of the motion and lags it by 45 degrees, and a fifty-micron droplet at a kilohertz is following two per cent of what it is supposed to be measuring.

regimes · Particle Eight numbers, one construction. The dimensionless groups this collection has produced, placed on a logarithmic axis at a representative value. Each is a memory time divided by a process time, each was named separately in a different field, and each decides the same question: whether the past is still present.

Every memory number is one time over another

These essays produced eight dimensionless groups in eight different fields, named after eight different people, spanning a factor of four hundred in value. Written out, all eight are a memory time divided by a process time, and all eight govern the same curve.

regimes · Dimensional

Named alongside it

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

ConvolutionMeasurementMemory kernelModel validityRegimeRelaxation timeStokes numberTurbulenceAnisotropyClosureDeborah numberDimensional analysis

All concepts