2024/08/14 by Verma, Mahendra K. · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2408.07573
Hydrodynamic turbulence exhibits nonequilibrium behaviour with k-5/3 energy spectrum, and equilibrium behaviour with kd-1 energy spectrum and zero viscosity, where d is the space dimension. Using recursive renormalization group in Craya-Herring basis, we show that the nonequilibrium solution is valid only for d < 6, whereas equilibrium solution with zero viscosity is the only solution for d>6. Thus, d=6 is the critical dimension for hydrodynamic turbulence. In addition, we show that the energy flux changes sign from positive to negative near d=2.15. We also compute the energy flux and Kolmogorov's constants for various d's, and observe that our results are in good agreement with past numerical results.