Inertia-induced coherent structures in a time-periodic viscous mixing flow

Abstract

Inertia-induced changes in transport properties of an incompressible viscous time-periodic flow due to fluid inertia (nonzero Reynolds numbers Re) are studied in terms of the topological properties of volume-preserving maps. In the noninertial Stokes limit (vanishing Re), the flow relates to a so-called one-action map. However, the corresponding invariant surfaces are topologically equivalent to spheres rather than the common case of tori. This has fundamental ramifications for the response to small departures from the noninertial limit and leads to a new type of response scenario: resonance-induced merger of coherent structures. Thus several coexisting families of two-dimensional coherent structures are formed that make up two classes: fully closed structures and leaky structures. Fully closed structures restrict motion as in a one-action map; leaky structures have open boundaries that connect with a locally chaotic region through which exchange of material with other leaky structures occurs. For large departures from the noninertial limit the above structures vanish and the topology becomes determined by isolated periodic points and associated manifolds. This results in unrestricted chaotic motion.