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Related Experiment Video

Updated: Sep 24, 2025

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
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Continuing invariant solutions towards the turbulent flow.

E Parente1,2, M Farano1,2, J-Ch Robinet2

  • 1Department of Mechanics, Mathematics and Management, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|May 9, 2022
PubMed
Summary
This summary is machine-generated.

A new mathematical framework reveals statistically invariant coherent solutions in turbulent channel flow. These solutions mimic real turbulent structures at larger scales, offering insights into fluid dynamics.

Keywords:
invariant solutions of the Navier–Stokes equationsturbulent flows

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Area of Science:

  • * Fluid Dynamics
  • * Turbulence Theory
  • * Mathematical Physics

Background:

  • * Understanding coherent structures in turbulent flows is crucial for predicting and controlling fluid behavior.
  • * Existing models often simplify or overlook the complex interplay of fluctuations around mean flow patterns.

Purpose of the Study:

  • * To develop a novel mathematical framework for characterizing coherent motion in turbulent channel flow.
  • * To identify statistically invariant solutions of the unsteady Reynolds-averaged Navier-Stokes equations.

Main Methods:

  • * Utilized a perturbative approach to the Reynolds-averaged Navier-Stokes equations.
  • * Employed a continuation procedure, gradually increasing turbulent eddy viscosity.
  • * Approximated the Reynolds stress tensor to recover flow solutions.

Main Results:

  • * Identified statistically invariant coherent solutions sustained by the Reynolds stress tensor.
  • * Observed that for small scales, solutions resemble Navier-Stokes invariant solutions.
  • * Found that for larger scales, solutions exhibit structures, wavelengths, and scaling similar to turbulent flows.

Conclusions:

  • * The proposed framework successfully characterizes coherent motion in turbulent channel flows.
  • * The recovered solutions provide a link between laminar and turbulent flow dynamics.
  • * This approach offers a new perspective on the statistical properties of turbulent structures.