Alan Powell
Dept. of Mech. Eng., Univ. of Houston, Houston, TX 77204-4792
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.