Energy spectrum in the enstrophy transfer range of two-dimensional forced turbulence

Numerical simulations of two-dimensional forced turbulence suggest that the enstrophy transfer range energy spectrum E(k) a little steeper than k−3 is robust in the sense that it may be realized in a wave number range under different run conditions. It is shown that such energy spectra fit well E(k)=CKη2/3k−3[ln(k/k1)]−1/3, where CK is a dimensionless constant, η the enstrophy transfer rate per unit mass and k1 a wave number at the bottom of the range. The simulations give CK≈1.9 in fairly good agreement with the existing theoretical estimates.