Comparative numerical-experimental analysis of the universal impact of arbitrary perturbations on transport in three-dimensional unsteady flows.

Numerical studies of three-dimensional (3D) time-periodic flow inside a lid-driven cylinder revealed that a weak perturbation of the noninertial state (Reynolds number Re=0) has a strong impact on the Lagrangian flow structure by inducing transition of a global family of nested spheroidal invariant surfaces into intricate coherent structures consisting of adiabatic invariant surfaces connected by tubes. These tubes provide paths for passive tracers to escape from one invariant surface to another. Perturbation is introduced in two ways: (i) weak fluid inertia by nonzero Re∼O(10(-3)); (ii) small disturbance of the external flow forcing. Both induce essentially the same dynamics, implying a universal response in the limit of a weak perturbation. Moreover, we show that the motion inside tubes possesses an adiabatic invariant. Long-term experiments were conducted using 3D particle-tracking velocimetry and relied on experimental imperfections as natural weak perturbations. This provided first experimental evidence of the tube formation and revealed close agreement with numerical simulations. We experimentally validated the universality of the perturbation response and, given the inevitability of imperfections, exposed the weakly perturbed state as the true "unperturbed state" in realistic systems.

Observability of periodic lines in three-dimensional lid-driven cylindrical cavity flows.

This study employs three-dimensional particle-tracking velocimetry (3D-PTV) for experimental investigation of the existence and properties of periodic lines in 3D lid-driven time-periodic flows inside a cylindrical cavity. These periodic lines, consisting of material points that periodically return to their initial position, play a central role in the transport properties of laminar flows, yet their existence has so far been demonstrated only in numerical simulations. The formation and characteristics of periodic lines are inextricably linked with spatiotemporal symmetries of the flow. 3D-PTV measurements determined that relevant symmetries, identified with previous symmetry analyses, are satisfied within experimental error bounds. These measurements subsequently isolated periodic lines in the designated symmetry planes, thus offering first experimental evidence of their physical existence and their fundamental reliance on symmetries. Experimental periodic lines are topologically equivalent to those in simulated flows with identical symmetries and exhibit the same response to changes in forcing conditions. The laboratory experiments by these observations bridge the gap from theoretical and numerical predictions on periodic lines to real 3D flows.

Scaling and asymmetry in an electromagnetically forced dipolar flow structure.

A dipolar flow structure is experimentally studied in a layer of salt solution driven by time-independent electromagnetic forcing. In particular, the response of the flow to the forcing is quantified by measuring the Reynolds number Re as a function of the Chandrasekhar number Ch (the ratio of Lorentz forces to viscous forces) and δ (the ratio of vertical to horizontal length scales of the flow domain). In agreement with theoretical predictions, two scaling regimes are found: Re~Ch/π(2) (viscous regime) and Re~Ch(1/2)δ(-1) (advective regime). The transition between the two regimes at Ch(1/2)δ~π(2) is reflected in the flow geometry in the form of an asymmetry of the dipolar flow structure.