Turbulence at zero Reynolds number should be impossible. Reynolds number measures the ratio of inertial to viscous forces; turbulence in classical fluids requires inertia to dominate. Bacterial suspensions operate at Reynolds numbers so small that inertia is irrelevant — a bacterium that stops swimming halts within a body length. Yet dense bacterial suspensions produce flows that look turbulent: chaotic vortices, energy cascades, intermittent statistics. The name “active turbulence” captures the visual resemblance while flagging the mechanistic difference.
Sahoo, Mukherjee, and Ray (2602.22044) push this analogy further by asking what happens when the activity itself is heterogeneous and dynamic. Previous models of active turbulence assumed uniform activity — every point in the fluid is equally active. Real bacterial suspensions aren't like this. Bacteria cluster. Activity varies in space. And the flow advects the bacteria, which changes the spatial distribution of activity, which changes the flow.
Their model treats activity as a dynamical field coupled to the Toner-Tu-Swift-Hohenberg equations. Activity is not a parameter but a variable. It has its own dynamics — advection by the flow, diffusion, and possibly sources and sinks. The flow generates activity gradients; the activity gradients modify the flow.
The consequences of this coupling are qualitatively new. Sharp activity fronts form — boundaries between regions of high and low activity. Turbulent motion becomes confined to high-activity regions. The interfaces between active and quiescent domains develop complex morphologies. The system exhibits transient coexistence of distinct spectral regimes — energy cascading differently in different spatial regions simultaneously.
This is where the analogy to classical turbulence breaks down productively. In classical turbulence, the energy injection is typically spatially uniform or at least statistically stationary. The cascade proceeds from large to small scales (or small to large in 2D) everywhere. In active turbulence with advected activity, the cascade is local — it operates differently in different places because the driving is different in different places. Universality, if it exists, is a local and time-dependent property rather than a global one.
The broader point is about the relationship between driving and response in nonequilibrium systems. In equilibrium, you can characterize a system by its temperature — a single number describing the intensity of fluctuations. In active turbulence with uniform activity, you can characterize it by the activity level — an analog of temperature for the nonequilibrium setting. With heterogeneous activity, there is no single characterization. The system is different places simultaneously. The turbulence is not one thing — it is a patchwork of local regimes stitched together by the advection that couples them.
The experimental implications are specific: in bacterial colonies near surfaces (where clustering is common), the spectral statistics of the flow should vary spatially. Near the center of a colony, one scaling regime. Near the edge, another. The transition between regimes is not a phase boundary but a gradient in activity, and the flow itself maintains and reshapes that gradient. Measurement would require simultaneous spatially-resolved velocity and concentration fields — technically challenging but achievable with current particle image velocimetry and fluorescence microscopy.