1. F. W. Matting, D. Chapman, J. Nyholm, and A. Thomas, NASA Technical Report R-82 (1960).
2. Correlated incompressible and compressible boundary layers
3. There is always the possibility that the usual boundary-layer approximation for the stress tensor may fail under certain conditions. In addition, there is room for argument about the importance in high-speed turbulent flows of various correlation terms (involving fluctuations in density, temperature, or viscosity) which are neglected here in order to treat the mean value of a product such as ρu or ρT (but not necessarily ρυ) as a product of mean values.
4. The author is aware that there exists no general affine transformation which is compatible with the experimental evidence and which allows the reduction of the turbulent boundary-layer equations to ordinary differential equations, as for laminar flow. The term similarity is used here in a broader sense not requiring uniform validity for the whole of the flow.
5. An identical result is obtained if the flow at infinity is assumed to be a uniform stream, but the condition onȳseems to be unnecessary if the flow is bounded at infinity by a fluid at rest. A closer examination of this case,i.e., of the jet entering a stagnant fluid, is not undertaken here. Even for the other cases mentioned the transformation in question may not be the most general or the most useful one which can be found; first, because the sufficient conditions used to bound the right-hand side of Eq. (2.6) for largeȳhave not been shown to be necessary, and second, because these conditions have been applied not only for largeȳbut throughout the barred flow. Furthermore, it has not been proved that the two flows involved in the transformation must always have the same character, i.e., that if one flow is a wake, so is the other; if one flow is a boundary layer with pressure gradient and mass transfer, so is the other; and so on. On the other hand, the transformation considered here is more general than any that has been considered previously, and has several properties that will prove to be useful in any study of turbulent flow. The possibility of a more general transformation is therefore not investigated further.