Turbulence at Low Reynolds Numbers

TL;DR

This paper demonstrates that turbulence, characterized by energy transfer across scales, can occur at low Reynolds numbers (~1) in quasi-2D flows, challenging the traditional view that turbulence requires high inertial forces.

Contribution

It introduces a new regime of turbulence at low Re by showing energy flux persists through stress-flow interactions in electromagnetic forced flows.

Findings

Spectral energy flux can be amplified at Re ~ 1

Turbulence can be driven without inertial dominance

New strategies for multiscale transport in low-Re flows

Abstract

Turbulence -- ubiquitous in nature and engineering alike [1-5] -- is traditionally viewed as an intrinsically inertial phenomenon, emerging only when the Reynolds number (Re), which quantifies the ratio of inertial to dissipative forces [6], far exceeds unity [7, 8]. Here, we demonstrate that strong energy flux between different length scales of motion -- a defining hallmark of turbulence [9] -- can persist even at Re ~ 1, thereby extending the known regime of turbulent flows beyond the classical high-Re paradigm. We show that scale-to-scale energy transfer can be recast as a mechanical process between turbulent stress and large-scale flow deformation. In quasi-two-dimensional (quasi-2D) flows driven by electromagnetic forcing, we introduce directionally biased perturbations that enhance this interaction, amplifying the spectral energy flux by more than two orders of magnitude, even in the absence of dominant inertial forces. This study establishes a new regime of 2D Navier-Stokes (N-S) turbulence, challenging long-standing assumptions about the high Re conditions required for turbulent flows. Beyond revising classical belief, our results offer a generalizable strategy for engineering multiscale transport in flows that lack inertial dominance, such as those found in microfluidic [10, 11] and low-Re biological [12-15] systems.