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February 10, 2026Open Access

The Signature of Chaos

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Authors

PSPirolo Andrés Sebastián

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Overview

Novel methodology quantifies turbulent flow complexity, suggesting a new theoretical framework for fluid dynamics.

Key Points

  • This work aims to establish a new method for detecting the transition from laminar to turbulent flow using information theory and local metrics.
  • Utilized Smoothed-Particle Hydrodynamics (SPH) simulations of flow over airfoil profiles and spherical obstacles.
  • Developed a local metric based on Shannon entropy in three-dimensional velocity fields.
  • Analyzed the Local Entropy Index (LEI) in relation to Reynolds numbers and phase transitions.
  • LEI showed a sharp, non-linear increase at critical Reynolds numbers signifying turbulence.
  • Observed complex spatial structures like vortex rings and helical instabilities were characterized by LEI.
  • LEI demonstrated convergence across various simulation scales, confirming its robustness as a chaos detector.

Cite This Study

Pirolo Andrés Sebastián (2025) studied this question.

synapsesocial.com/papers/698acac07c832249c30ba0bbhttps://doi.org/10.5281/zenodo.18523027
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  1. 1Emergence Inevitability and Algebraic Computational Methods of Turbulence Based on Discrete Microscopic Causal Statistics and Multidimensional Manifold Reconstruction2026
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  4. 4A topology-based method for assessing the complexity and unpredictability of unsteady flows2025
  5. 5Li's Intrinsic Scale and Equilibrium Transition Theory: A Universal Mechanism for Fluid Stability and Turbulence Transition2026