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

Sound absorption — where it appears

The loss of acoustic energy as a sound wave travels, by viscosity, heat conduction and the slow relaxation of molecular vibrations in the gas. It rises steeply with frequency, which is why distant thunder rumbles and why the front of a sonic boom is spread over a millisecond.

Named by 3 essays across 2 fields — 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 Dry air makes a slow bang. The 10-to-90 per cent rise time of a steady shock against relative humidity, for jumps of 25, 50 and 90 pascals, all below the strength at which a discontinuity returns. Each falls roughly as the nitrogen relaxation time does, and doubles when the jump is halved. The rule marks the thermoviscous rise time of the 50-pascal shock, a few microseconds — two to three orders of magnitude below any of the curves.

Oxygen makes a boom's crack, nitrogen its rise time

The shock at the front of a sonic boom is not the viscous shock of a textbook, a few microseconds thick. It is spread over a large fraction of a millisecond by the vibrational relaxation of the air's molecules, and the two gases do different jobs. Oxygen, fast, removes the discontinuity for any boom weaker than about ninety pascals and decides how much of the front is left at the frequencies the ear weighs most; nitrogen, slow, sets the rise time that is measured. Water vapour speeds both, so a dry day makes a softer bang.

compressible · Sonic boom 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 viscosityCompressibilityDispersionDissipationModel limitRelaxationShock structureTransport coefficientAcousticsDiscontinuityDissipation functionEntropy

All concepts