2017/08/11 by David Weyburne, Weyburne, David W.
Engineering · Earth and Planetary Sciences · Environmental Science · #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Wind and Air Flow Studies
paper · pdf · doi:10.48550/arxiv.1708.03547
Using the flow governing equation approach to similarity, Weyburne (D.\nWeyburne, arXiv:1701.02364, 2016) recently showed that for 2-D turbulent\nboundary layer flows, the Prandtl Plus scalings are NOT, in general, the proper\nsimilarity scaling parameters. Based on that failure, Weyburne proposed\nalternative length and velocity scaling parameters that satisfy the flow\ngoverning approach to similarity for external turbulent boundary layer flows.\nHerein, we show that both the proposed new scalings and the Prandtl Plus\nscalings have a theoretical underpinning which requires that the boundary layer\nmust show whole profile similarity for the scalings to be applicable. The\nproblem is that wall-bounded turbulent boundary layers are generally\nacknowledged as not showing whole profile similarity under any circumstances.\nThus, applying scaling parameters that subsume whole profile similarity to\nboundary layers that do not show whole profile similarity means that, at best,\nthe result represents a good approximation. Computer simulation results are\nused to explore these issues and provides at least preliminary experimental\nsupport of the theoretical failures.\n