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

Abstract

Beyond a critical Toner--Tu drive, bacterial turbulence exhibits universal statistics, including a parameter-independent energy spectrum E(k)∼ 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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BibTeX RIS

BibTeX

@misc{kumar2026reynoldslike,
  title = {{A Reynolds-like Criterion for the Onset of Universal Active Turbulence}},
  author = {Kunal Kumar and Sandip Sahoo and Kirti Kashyap and Amal Manoharan and Siddhartha Mukherjee and Anupam Gupta and Samriddhi Sankar Ray},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39999},
  eprint = {2609.39999},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39999},
  note = {CC BY-NC-ND 4.0},
}

RIS

TY  - UNPB
TI  - A Reynolds-like Criterion for the Onset of Universal Active Turbulence
AU  - Kunal Kumar
AU  - Sandip Sahoo
AU  - Kirti Kashyap
AU  - Amal Manoharan
AU  - Siddhartha Mukherjee
AU  - Anupam Gupta
AU  - Samriddhi Sankar Ray
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39999
UR  - https://arxiv.org/abs/2609.39999
AB  - Beyond a critical Toner--Tu drive, bacterial turbulence exhibits universal statistics, including a parameter-independent energy spectrum E(k)∼ 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.
ER  -

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