Renormalization-group analysis of two-dimensional incompressible turbulence

Abstract

The ${\mathit{k}}^{\mathrm{\ensuremath{-}}3}$ spectrum, including the logarithmic correction, for the enstrophy range and the ${\mathit{k}}^{\mathrm{\ensuremath{-}}5/3}$ spectrum for the energy range of two-dimensional turbulence are derived using the renormalization-group method. The values of the Kolmogorov constants C'\ensuremath{\simeq}1.59 in the enstrophy range and C\ensuremath{\simeq}6.45 in the energy range are obtained without the need of adjustable parameters.