Anomalous Transport in Steady Plane Viscous Flows: Simple Models
Steady laminar plane flows of incompressible viscous fluids past lattices of solid bodies or arrays of soft obstacles (steady vortices) are less trivial as they may seem to be. Dynamics of tracers in regular patterns of streamlines is often aperiodic: repeated slow passages near stagnation points and/or solid surfaces provide a mechanism for eventual decorrelation. Velocity spectra for such tracers are known to possess fractal component, whereas correlation functions, in spite of integrability of the underlying dynamical system, display algebraic decay. Singularities of passage times near the obstacles depend on the shape and boundary conditions (stress-free/no-slip); this has implications for existence and quantitative characteristics of subdiffusive and superdiffusive regimes of transport. Here, we study the transport properties with the help of the simple and computationally efficient model: the special flow. Characteristics of anomalous transport, computed for such flows, match well the theoretical estimates.
KeywordsViscous flow Stagnation points Anomalous transport Dynamic diffusion
The authors feel deeply obliged to M.I. Rabinovich for his tireless proliferation of dynamical system approach to various fields of science. This research was supported by a Grant from the GIF, the German-Israeli Foundation for Scientific Research and Development, Grant I-1271-303.7/2014.
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