The asymptotic structure of high-Reynolds number boundary layers

The methodology of matched asymptotic expansions or "generalized boundary layer theory" for large Reynolds number Re, (based on friction velocity and outer length scale), pioneered by Prandd [1], is used to extract from measured or computed mean velocity profiles in turbulent channel and pipe flows their limiting behavior at infinite Re-tau After fitting an "outer expansion" in terms of suitable functions of the outer wall-normal coordinate eta to the data, the construction of composite expansions is used "in reverse" to extract the "inner expansion". Its leading term of order O(Re-tau(0)) represents the near-wall solution for infinite Re-tau which is found to be identical for channels and pipes. For large values of the inner wallnormal coordinate y(+) this limiting inner expansion for the strearnwise velocity is furthermore shown to be well described by Prandtl's famous "log-law".