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.