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λ-Navier-Stokes turbulence.

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  • 1Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Paris 75005, France.

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Summary
This summary is machine-generated.

Researchers explored a modified Navier-Stokes model, altering energy cascade direction with a parameter λ. Near a critical point, kinetic energy diverges, reducing intermittency and revealing a new turbulent state.

Keywords:
intermittencyinverse cascadephase transitionturbulence

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Area of Science:

  • Fluid Dynamics and Turbulence
  • Computational Physics

Background:

  • The Navier-Stokes equations describe fluid motion, but their complex behavior, especially in turbulent regimes, remains a significant challenge.
  • Previous work introduced a parameter λ to the Navier-Stokes equations, allowing variation of homochiral vs. heterochiral interaction weights while preserving symmetries.

Purpose of the Study:

  • To numerically investigate the impact of varying the parameter λ on energy cascade direction and turbulent properties.
  • To explore the behavior of kinetic energy, energy spectra, and fluxes near a critical value of λ.

Main Methods:

  • Numerical simulations of the modified Navier-Stokes equations with varying λ and Reynolds number (Re).
  • Analysis of kinetic energy, energy spectra, and forward/inverse energy fluxes.
  • Investigation of intermittency and fluctuations near the critical point.

Main Results:

  • A critical value of λ was identified, leading to a change in energy cascade direction.
  • Kinetic energy diverges with a specific scaling law as Re approaches the critical point.
  • Energy spectra show an increased bottleneck effect with decreasing λ; fluxes exhibit large fluctuations near the critical point, and intermittency is reduced.

Conclusions:

  • The study reveals a novel critical point in Navier-Stokes turbulence, characterized by diverging kinetic energy and reduced intermittency.
  • A new stationary state with high-amplitude opposing fluxes is observed near this critical point.
  • The findings suggest a potential statistical description of turbulence as an expansion around this critical point.