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A wave that dies within one wavelength — 100 Hz in air

A wave that dies within one wavelength — 100 Hz in air
A wave that dies within one wavelength — 100 Hz in airThe velocity profile above an oscillating wall, at eight phases of one cycle, with depth in units of δ = √(2ν/ω). The motion is a wave travelling *into* the fluid, and its amplitude falls by 1/e in the same distance it turns by one radian — so it is dead within about one wavelength, and the fluid three δ up hardly knows the wall is moving at all. This is one of the very few exact solutions the Navier–Stokes equations have. The dashed line is one fixed distance above the wall in millimetres: in these units it climbs as the square root of the frequency, which is the whole of how far the motion reaches.-1-0.500.5101234velocity, in units of the wall'sdepth, in units of δδ = 0.2185 mmperiod 10.00 msν = 0.000015 m²/seight phases of one cyclethe heavy line is t = 0the dashed line is 0.327 mmabove the wall — 1.50 δ hereresidual of ∂u/∂t = ν∂²u/∂y²3.5e-9Stokes' second problem — exact, with the diffusion equation differenced off itf = 100 Hz, ν = 0.000015 m²/s · laminar, no mean flow

The velocity profile above an oscillating wall, at eight phases of one cycle, with depth in units of δ = √(2ν/ω). The motion is a wave travelling *into* the fluid, and its amplitude falls by 1/e in the same distance it turns by one radian — so it is dead within about one wavelength, and the fluid three δ up hardly knows the wall is moving at all. This is one of the very few exact solutions the Navier–Stokes equations have. The dashed line is one fixed distance above the wall in millimetres: in these units it climbs as the square root of the frequency, which is the whole of how far the motion reaches.

13 essays call oscillating-wall. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

It is also the blast radius. Changing oscillating-wall changes every figure listed here at once, and on this site it may change what they assert as well as what they show — which is what has to be rebuilt and looked at before the change is believed.

Where it is called

What each of these essays asks for instead of the defaults is on the regime index, which reads the parameters back out of the finished figures rather than out of the placements.

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