Inertial range of two-dimensional turbulence in a Lagrangian renormalized approximation

Abstract

The inertial range structure of two-dimensional turbulence is studied on the basis of a deductive Lagrangian renormalized approximation. The approximation is consistent with the energy spectra E(k)=Cε2/3 k−5/3 in the energy-transfer range and E(k)=C′β2/3 k−3 ×[ln(k/k1)]−1/3 (k≫k1) in the enstrophy-transfer range, and yields the estimates C=5.88 and C′=1.44. Here E(k) is the usual energy spectrum, ε and β are, respectively, the rates of energy and enstrophy transfer per unit mass, and k1 is the bottom of the enstrophy-transfer range.