### ASA 125th Meeting Ottawa 1993 May

## 2aEA8. Concerning the ``displacement thickness theory'' of boundary layer
noise.

**Alan Powell
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*Dept. of Mech. Eng., Univ. of Houston, Houston, TX 77204-4792
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The streamlines just outside a boundary layer are pushed away from the
wall by the displacement thickness (delta)* as the flow slows down.
Hydrodynamic fluctuations in (delta)* have been considered to act as a compact
monopole source distribution at the edge of the boundary layer, see Laufer et
al. (1964), Lauchle (1981, 1989), Sornette and Lagier (1984, 1986). However,
Rayleigh's (normal velocity) formula applied to a plane just outside the layer
reduces to the (delta)* theory only if the acoustic (sound-speed-dependent)
contribution of the fluctuations there, due to the sound sources that must be
within the layer, can be safely ignored. For a monopole source the (delta)*
theory yields the correct result, although the net strength must be zero
(because of continuity), except for viscous dissipation effects. It also yields
the correct results for tangential dipoles, pertinent to net wall shear
stresses, and for tangential longitudinal quadrupoles. But the (delta)* theory
cannot represent normal longitudinal quadrupoles, an essential complementary
component of plane boundary layer noise, Powell (1991): the extensive
(noncompact) acoustic field contribution to the plane source distribution is
then essential.