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Critical dimension for hydrodynamic turbulence.

Mahendra K Verma1

  • 1Department of Physics, <a href="https://ror.org/05pjsgx75">Indian Institute of Technology Kanpur</a>, Kanpur 208016, India.

Physical Review. E
|October 19, 2024
PubMed
Summary
This summary is machine-generated.

Hydrodynamic turbulence transitions between nonequilibrium and equilibrium states. A critical dimension of d=6 was identified, impacting energy spectra and flux behavior in fluid dynamics.

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Area of Science:

  • Fluid Dynamics
  • Statistical Physics
  • Turbulence Theory

Background:

  • Hydrodynamic turbulence displays distinct energy spectra based on equilibrium and nonequilibrium states.
  • The behavior is influenced by space dimension (d) and viscosity.

Purpose of the Study:

  • To determine the critical dimension for hydrodynamic turbulence.
  • To analyze the energy spectrum and flux behavior across different dimensions.

Main Methods:

  • Recursive renormalization group in the Craya-Herring basis.
  • Analysis of equilibrium and nonequilibrium solutions for varying space dimensions.

Main Results:

  • The nonequilibrium solution is valid for d<6; the equilibrium solution with zero viscosity dominates for d>6.
  • d=6 is identified as the critical dimension for hydrodynamic turbulence.
  • Energy flux sign reversal observed near d=2.15; energy flux and Kolmogorov's constants computed for various d.

Conclusions:

  • The study establishes d=6 as the critical dimension, unifying turbulence behavior across dimensions.
  • The findings provide a comprehensive understanding of energy transfer and spectral properties in hydrodynamic turbulence.
  • Computed constants align well with existing numerical data, validating the theoretical approach.