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A Model of Interacting Navier-Stokes Singularities.
Hugues Faller1, Lucas Fery1,2, Damien Geneste1
1Service de Physique de l'État Condensé, CNRS UMR 3680, CEA, Université Paris-Saclay, 91190 Gif-sur-Yvette, France.
Entropy (Basel, Switzerland)
|July 27, 2022
Summary
We introduce pinçons, interacting singularities of Navier-Stokes equations, to model fluid dynamics. These pinçons exhibit complex behaviors like repulsion, collapse, and orientation under stochastic forcing, offering insights into turbulence.
Area of Science:
- Fluid Dynamics
- Mathematical Physics
- Turbulence Theory
Background:
- Navier-Stokes equations describe fluid motion but are complex to solve.
- Existing models like Novikov's vorton model simplify Euler equations.
- Understanding singularities is crucial for turbulence research.
Purpose of the Study:
- Introduce a novel model of interacting singularities for Navier-Stokes equations, named pinçons.
- Generalize existing models to include dissipation and non-equilibrium dynamics.
- Investigate the behavior of interacting pinçons under various conditions.
Main Methods:
- Developed a model of interacting singularities (pinçons) obeying local Navier-Stokes equations.
- Studied pinçon dynamics, including pairs, dipoles, and interactions with regular fields.
- Analyzed behavior under stochastic forcing and arbitrary intensity/orientation.
Main Results:
- Pinçons exhibit non-equilibrium dynamics and generalize the vorton model.
- A pinçon dipole shows initial repulsion, followed by dissipation.
- Observed collapse, dipolar anti-aligned runaway, and anisotropic aligned runaway dynamics.
- Pinçon collapse mirrors vortex ring reconnection characteristics and Leray scaling.
Conclusions:
- The pinçon model provides a framework for studying interacting singularities in Navier-Stokes flows.
- Pinçon dynamics reveal insights into turbulence, dissipation, and non-equilibrium states.
- The model captures key features of vortex dynamics and reconnection.
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