A base for the log law and von Karman's constant problem. Issue 6 (2nd November 2022) - Smart, Graeme
Abstract : The log-law profile equation and its intrinsic von Karman's constant are widely used in fluid mechanics. Despite numerous theoretical and empirical attempts to establish formal bases for these concepts, no consensus has been reached. We review past work and present a simple rolling eddy model of boundary-layer turbulence. We consider fluid momentum loss from eddies that roll out over smaller eddies on a timescale that matches the shear interaction of the eddies with the boundary. The resulting parametric form for eddy scaling provides a basis for comprehending turbulent boundary-layer flow as an exponential growth process. The outward-rolling-eddy model formulation yields a log law and explanation for von Karman's constant. Results of the model are compared with instantaneous flow imagery and direct numerical simulations. The model implies that changes in von Karman's constant indicate changes in the underlying eddy self-similarity pattern. The approach gives a new perspective on an old problem.