Low Reynolds number turbulence: Tensor Geometry Drives Turbulence in the Diminishing of Inertia

Turbulence is widely regarded as an intrinsically inertial phenomenon—arising only when the Reynolds number (Re), which quantifies the ratio of inertial to dissipative forces, far exceeds unity. Here, we demonstrate that strong spectral energy flux—a defining hallmark of turbulence—can be sustained at Re ≈ 1, thereby extending the known regime of turbulent flows beyond the classical high-Re paradigm. We develop a tensorial framework in which scale-to-scale energy transfer is recast as a mechanical process between the turbulent stress and rate of strain tensors. In quasi-two-dimensional flows driven by electromagnetic forcing, we introduce directionally biased perturbations that align these tensors, 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 two-dimensional Navier–Stokes (N-S) turbulence, challenging long-standing assumptions about the high Reynolds number conditions required for turbulent flows. Beyond challenging classical assumptions, our results offer a generalizable strategy for engineering multiscale transport in flows that lack inertial dominance, such as those found in microfluidic and biological systems.