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

Relaxation — where it appears

The return of a system towards equilibrium after a disturbance, over a characteristic time. When a disturbance is repeated faster than that time the system cannot follow, and the lag between them appears as dissipation.

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

The coefficient Stokes threw away is not a correction. What absorbs sound in dry air, split into the three transport effects that add to make the diffusivity of sound. Shear viscosity is the largest single contribution and it is not most of it; the bulk viscosity — which Stokes set to zero in 1845, saying in the same paper that he had no argument for doing so — is a quarter, and thermal conduction is a fifth. Setting ζ to zero does not make a small error in the absorption; it makes a 24 per cent one.

The viscosity nobody uses

A fluid has two viscosities. One resists a change of shape and appears in every viscous calculation; the other resists a change of volume, was set to zero by Stokes in 1845 in a paper that says he had no argument for doing so, and for carbon dioxide is fifteen hundred times larger than the one everybody quotes.

viscous · Bulk viscosity On Mars the bulk viscosity is two speeds of sound. The speed of sound in carbon dioxide at 610 pascals and 240 kelvin against frequency, with the bulk viscosity scaled from its value at one atmosphere by pressure alone. Low notes travel at 245 m/s, with the bending vibration keeping up; high ones at 252 m/s, with it frozen. The step is centred near 342 Hz. The Perseverance rover's microphones reported the same thing in 2022: two speeds of sound, near 240 and 250 metres a second, either side of a few hundred hertz.

The largest bulk viscosity is the first to expire

A bulk viscosity is not a separate property of a gas. It is the time a molecule's internal motion takes to catch up with a compression, multiplied by the pressure and by how much heat capacity lags, and read from below that time's frequency. So the coefficient that is largest is the one that stops being a coefficient soonest: carbon dioxide's fifteen-hundred-fold value is ten per cent wrong at 24 kHz, and on Mars it is two speeds of sound in the audible band.

viscous · Bulk viscosity

Named alongside it

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

Bulk viscosityCompressibilityDissipationSound absorptionTransport coefficientDispersionDissipation functionEntropyModel limitRate of strainShock structure

All concepts