Modified Hierarchy Structure of Rough-Wall Flows
Analysis of the mean differential force balance reveals that the characteristic properties of wall-bounded turbulent flows (e.g., the logarithmic mean profile and distance-from-the-wallscaling) arise owing to the existence of an internal layer hierarchy. Mathematically, this hierarchical structure is formally admitted by the appropriately simplified Reynolds Averaged Navier–Stokes (RANS) equation. Physically, its existence accounts for the dynamics undergoing a continuous self-similar (approximately) variation in scale over the range ν ∕ u τ≤ ℓ≤ δ. These findings lead to the hypothesis that surface roughness modifies this mean dynamical structure through the imposition of new length scales. The present study explores aspects of this hypothesis.
KeywordsLayer Hierarchy Length Scale Distribution Roughness Crest Quality Boundary Layer Turbulent Inertia
The authors would like to thank S. Hoyas, J. Jiménez, B. McKeon and M. Shockling for making their data available. The support of the ONR (N000140810836, grant monitor Ronald Joslin) is gratefully acknowledged.
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