Memory-Induced Curvature Drives Irreversible Transport in Irrotational Flows

TL;DR

This paper demonstrates that memory effects in irrotational flows create a geometric mechanism for irreversible transport, independent of vorticity or symmetry breaking, through curvature induced by history-dependent velocity gradients.

Contribution

It introduces a novel geometric mechanism driven by memory-induced curvature for irreversible transport in irrotational flows, expanding understanding beyond traditional vorticity-based explanations.

Findings

Memory-induced curvature causes measurable loop displacements.

Scaling with phase mismatch parameter matches experimental data.

Irreversible transport arises from geometric effects, not vorticity.

Abstract

Irreversible transport in time-periodic flows is commonly attributed to vorticity, nonlinear forcing, or symmetry breaking. We show that finite-memory reconstruction of the velocity gradient generates a purely geometric mechanism for transport even when the instantaneous flow remains locally irrotational at all times. Memory promotes the velocity gradient to a history-dependent connection along particle trajectories whose noncommutativity produces a finite curvature over one forcing cycle. The associated holonomy generates a measurable loop displacement controlled solely by the dimensionless parameter {\omega}{\tau}_m, which quantifies the phase mismatch between forcing and reconstruction. The predicted scaling is consistent with independently reported measurements across distinct oscillatory flow configurations, supporting the interpretation of memory-induced curvature as a minimal geometric origin of irreversible transport in periodically driven continua.