### ASA 127th Meeting M.I.T. 1994 June 6-10

## 4aEA13. More on flow fields driving a contiguous acoustic field---A simple
physical argument in terms of vorticity alone, yielding Mohring' form.

**Alan Powell
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*Dept. of Mech. Eng., Univ. of Houston, Houston, TX 77204-4792
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In J. Acoust. Soc. Am. 36, 830--832 (1964): ``The sound radiation from a
slightly compressible [compact] flow can be calculated by estimating the
pressure that would exist at an enclosing [spherical] surface just as if the
fluid were incompressible, this [hydrodynamic] pressure then being inserted in
the appropriate point-multipole expression for the sound radiation in the
[surrounding] compressible fluid...the [resultant] far field sound pressure is
the same as for the theory of vortex sound,'' for which the quadrupole strength
contribution is the volume integral of y[sub x] ((zeta)xu)[sub x][sup ''],
where u=velocity, (zeta)=(cursive beta)xu=vorticity, y=coordinate in flow,
x=far-field point, ( )[sub x](identically equal to)(vector)(centered dot)x/x,
and ( )'(identically equal to)(cursive beta)/(cursive beta)t( ). Now work in
terms of induced velocity instead of pressure, starting with the so-called
Biot--Savart law. The result is the integral of (1/2)(yx(zeta)'')[sub x] for
the dipole contribution and of (1/3)y[sub x](yx(zeta)''')[sub x] for
quadrupoles. These involve only the vorticity and not the velocity. These final
results were first given by Mohring [J. Fluid Mech. 85, 685--691 (1978)] and
later by Kambe [J. Fluid Mech. 173, 643--681 (1986)], both using more complex
methods.