The Signature of Chaos
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Related Work
Other preprints by this author:
https://zenodo.org/records/17267849
https://zenodo.org/records/17239094
https://zenodo.org/records/17204948
https://zenodo.org/records/17096978
The Signature of Chaos, by Andrés Sebastián Pirolo
The transition from laminar to turbulent flow is a fundamental, yet incompletely understood, phenomenon in fluid dynamics. Traditional global metrics often fail to capture the local onset of chaos. In this paper, we propose a novel methodology based on information theory to quantify fluidic complexity. Using a Smoothed-Particle Hydrodynamics (SPH) simulation of a von Kármán wake, we demonstrate that a local, information-centric metric—the Shannon entropy of the velocity field—serves as a robust and unambiguous detector for the critical transition to turbulence.
Our results show a distinct phase transition where the Local Entropy Index (LEI) exhibits a sharp, non-linear increase as the Reynolds number crosses a critical threshold. This approach provides a more direct measure of the informational disorder inherent in turbulence than traditional methods and offers a new avenue for the prediction and analysis of complex system.
Andrés Sebastián Pirolo
Correspondence to: andrespirolo@gmail.com
Notes
This preprint introduces a novel information-theoretic method for predicting the onset of turbulence in solutions to the Navier-Stokes equations. The core of this work is the development of a Local Entropy Index (LEI), a quantitative tool that successfully detects the laminar-turbulent phase transition.
As an independent researcher, I am keen to share this work with the broader physics and mathematics communities to receive critical feedback and foster collaboration.
To facilitate this, I am currently seeking an endorsement to submit preprints to the arXiv.org repository. If you are an established researcher in a relevant field (such as Fluid Dynamics, Nonlinear Dynamics, or Mathematical Physics) and find this work compelling, I would be very grateful if you could contact me to consider providing an endorsement. This would be invaluable for the continuation and refinement of this research.
Contact: andrespirolo@gmail.com
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NS paper Pirolo 1_2.pdf
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