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A discussion of cone and flat-plate Reynolds numbers for equal ratios of the laminar shear to the shear caused by small velocity fluctuations in a laminar boundary layer

By use of the linear theory of boundary-layer stability and Schlichting's formula for the maximum amplification of a disturbance, an approximate relation is derived between the Reynolds number on a cone and the Reynolds number on a flat plate for equal closeness to transition. The indication is that the ratio of the cone Reynolds number for transition, based on the distance to the cone apex, to the plate Reynolds number for transition, based on the distance to the leading edge, is not in general equal to 3, as has been suggested by other investigators, but varies from 3 when transition occurs at the minimum critical Reynolds number to unity when transition occurs at a large multiple of the critical Reynolds number.

FLOW, TURBULENT↗

A general integral form of the boundary-layer equation for incompressible flow with an application to the calculation of the separation point of turbulent boundary layers

A general integral form of the boundary-layer equation, valid for either laminar or turbulent incompressible boundary-layer flow, is derived. By using the experimental finding that all velocity profiles of the turbulent boundary layer form essentially a single-parameter family, the general equation is changed to an equation for the space rate of change of the velocity-profile shape parameter. The lack of precise knowledge concerning the surface shear and the distribution of the shearing stress across turbulent boundary layers prevented the attainment of a reliable method for calculating the behavior of turbulent boundary layers.

Tetervin, Neal↗