  Using the flow governing equation approach to similarity, Weyburne (D.
Weyburne, arXiv:1701.02364, 2016) recently showed that for 2-D turbulent
boundary layer flows, the Prandtl Plus scalings are NOT, in general, the proper
similarity scaling parameters. Based on that failure, Weyburne proposed
alternative length and velocity scaling parameters that satisfy the flow
governing approach to similarity for external turbulent boundary layer flows.
Herein, we show that both the proposed new scalings and the Prandtl Plus
scalings have a theoretical underpinning which requires that the boundary layer
must show whole profile similarity for the scalings to be applicable. The
problem is that wall-bounded turbulent boundary layers are generally
acknowledged as not showing whole profile similarity under any circumstances.
Thus, applying scaling parameters that subsume whole profile similarity to
boundary layers that do not show whole profile similarity means that, at best,
the result represents a good approximation. Computer simulation results are
used to explore these issues and provides at least preliminary experimental
support of the theoretical failures.
