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

Resonance — where it appears

The large response of a system driven near one of its natural frequencies, where each cycle adds energy in step with the last. In pipes and elastic tubes it appears when reflected waves return in phase with the waves still arriving.

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

Captured, and not captured. The amplitude of the wake's oscillation over time, for a forcing inside the capture band and one outside it. Inside, the amplitude settles; outside, it beats at the difference between the two frequencies, because the wake is keeping its own time and the forcing is keeping its.

A wake told what to do

Force a shedding wake near its own frequency and it abandons its own and adopts the forcing's. The band over which it will do so is proportional to how hard it is pushed — and near the edge of the band it takes six times as long to make up its mind.

regimes · Strouhal One number decides which pulse grows. The pressure pulse and the flow pulse at the far end of the tube, each as a multiple of its value at the entrance, against the load's reflection coefficient. A load that reflects pressure with the same sign — a stiffer or narrower continuation — amplifies the pressure pulse and damps the flow pulse. One that reflects it inverted — a wider continuation, or many branches — does the opposite. With no reflection both fall slightly, by the wave's own attenuation. The two curves cross near Γ = 0 and pull apart on either side.

The pulse that grows as it leaves the heart

The pressure pulse measured at the wrist is larger than the pulse in the aorta that drives it, and the flow pulse is smaller. Nothing downstream is pumping. A wave reflected from the end of an elastic tube arrives back in step with the outgoing wave near the end and out of step near the start, and a single number — the reflection coefficient — decides whether it is the pressure or the flow that grows.

regimes · Womersley

Named alongside it

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

MeasurementDimensionless numberImpedanceLock-inMemory kernelModel limitModel validityOscillationOscillatorReflectionRegimeRelaxation time

All concepts