An Analysis of the Formation of Turbulent Patches in the Transition Boundary Layer

Abstract

An analysis is presented of the formation and motion of turbulent pressure patches under the transition boundary layer on a flat plate in a zero pressure gradient. The shape of the patch on the surface of the plate is assumed to be triangular with an area that increases as the patch moves downstream from its point of inception. The expressions for the cross-correlation and the cross-spectral density of the surface-pressure fluctuations which are obtained are both space and time dependent. A relation is shown to exist between the transition phenomena and the instabilities in the laminar boundary layer. Finally, the analytical results are used to determine the breakdown points of the laminar instabilities.