### ASA 125th Meeting Ottawa 1993 May

## 2aEA9. Aerodynamic noise theory---An alternative monopole source term.

**Alan Powell
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*Dept. of Mech. Eng., Univ. of Houston, Houston, TX 77204-4792
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Lighthill's equation for the acoustic pressure perturbation may expressed
as (open square)[sup 2]p=(rho)[sub 0](1/2(zeta)[sup 2]-e[sub ii][sup 2]), where
(rho)[sub 0] is the density of the incompressible inviscid noise generating
flow, (zeta) is its vorticity, and e[sub ii] is the principal strain rates. In
the hydrodynamic field ((del)[sup 2] vice (open square)[sup 2]), pressure
minima and maxima evidently always tend to occur in regions of vorticity
squared and strain rates squared, repectively. For the far field, it is proved
that the volume integral over the source region of the two monopole terms
cancel exactly: the net monopole strength is always zero. Here the source
region is not extensive as for the existing ``simple source'' theory. This is
readily demonstrated in the limiting case, a steady vortex. This supports the
gist of Ribner's 1964 intuitive sketch of turbulent flow eddies having central
pressure minima with the maxima in the regions of collision: the notion of the
dilatation in the center of a single vortex by itself being the source
(Legendre, 1992) is evidently incomplete. Quadrupole radiation may be studied,
in principle at least, by taking the second moment of the source strength, or
by considering the acceleration of the source field explicitly, say, a la
Lowson, 1965.