Transition noise—The role of fluctuating displacement thickness

The role of the fluctuating wall shear stress on the noise generated by incompressible boundary-layer transition was recently analyzed [G. C. Lauchle, J. Acoust. Soc. Am. 67, 158–168 (1980)]. The solutions of that analysis suggest that the shear stress mechanism generates hydrodynamic sound weakly in comparison to the sound generated by a fully developed turbulent boundary-layer flow. Because boundary-layer transition is a very unstable and nonsteady flow, we might expect that other acoustic mechanisms exist. In this paper, we examine one other; namely, that of the fluctuating boundary-layer displacement thickness which is expected to occur as turbulence bursts are created and convected over the surface. The analysis shows that a weak monopole sound source occurs, and at low subsonic flow velocities, this source generates significant acoustic energy. Comparisons of the theoretical predictions with available experimental data support this conclusion.