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arXiv · 2609.39999

A Reynolds-like Criterion for the Onset of Universal Active Turbulence

Kunal Kumar·Sandip Sahoo·Kirti Kashyap·Amal Manoharan·Siddhartha Mukherjee·Anupam Gupta·Samriddhi Sankar Ray
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Abstract

Beyond a critical Toner--Tu drive, bacterial turbulence exhibits universal statistics, including a parameter-independent energy spectrum $E(k)\sim k^{-3/2}$. We show that the same universal state can be reached not only by increasing activity, but also by strengthening nonlinear advection, weakening nonlinear saturation, or tuning the Swift--Hohenberg instability. Motivated by the competition between these processes, we identify the independent dimensionless groups governing the dynamics and construct a Reynolds-like control parameter from them. A single critical value, calibrated from the known activity-controlled transition, predicts the onset of universality along the other parameter routes and collapses them onto a common threshold. These results identify a dynamical organizing parameter for the onset of universal active turbulence and provide a Reynolds-like measure for the Toner--Tu--Swift--Hohenberg universality class.

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Kunal Kumar, Sandip Sahoo, Kirti Kashyap, Amal Manoharan, Siddhartha Mukherjee, Anupam Gupta, Samriddhi Sankar Ray. 2026-09-30. A Reynolds-like Criterion for the Onset of Universal Active Turbulence. https://arxiv.org/abs/2609.39999

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