Lagrangian turbulence and spatial complexity in a Stokes flow

Abstract

A simple Stokes flow problem, corresponding to an incompressible flow between two eccentric cylinders rotating alternately, is investigated numerically. It is demonstrated that for a wide range of system parameters the fluid particles can evolve along highly chaotic orbits, thereby providing an example of so called ‘‘Lagrangian turbulence.’’ Passive scalar distributions can rapidly evolve into structures of remarkable spatial complexity that can be characterized in terms of the underlying phase space dynamics. An investigation is made of the ability of simple area preserving mappings, deduced from the physical problem, to reproduce the dynamics obtained from the exact solution.