Geometric Memory Generates Irreversible Transport in Time-Periodic Irrotational Flows

TL;DR

This paper reveals that geometric memory effects in time-periodic irrotational flows can cause irreversible transport, independent of vorticity or nonlinear forcing, supported by experimental validation.

Contribution

It introduces a geometric mechanism for irreversible transport in irrotational flows, providing a closed-form expression and experimental validation without fitting.

Findings

Predicted scaling and magnitude match experimental data

Geometric memory is a minimal source of irreversibility

Irreversible transport occurs without vorticity or symmetry breaking

Abstract

Irreversible transport is generally attributed to vorticity, nonlinear forcing, or explicit symmetry breaking. We show that it can arise even in strictly time-periodic and locally irrotational flows through a purely geometric mechanism. By reconstructing the velocity gradient through causal self-transport over a finite memory time, deformation acquires the structure of a geometric connection whose holonomy generates a finite Lagrangian drift over one forcing cycle. The resulting contribution admits a closed-form, parameter-free expression. A quantitative consistency analysis using independently published experimental measurements shows that the predicted scaling and magnitude agree with observations without fitting or normalization. These results identify geometric memory as a minimal and generic source of irreversible transport.