Inertial-range transfer in two- and three-dimensional turbulence

A simple dynamical argument suggests that the k −3 enstrophy-transfer range in two-dimensional turbulence should be corrected to the form \[ E(k) = C^{} β21/3k⁻³[ln (k/k_1)]-1/3 (k k_1), \] where E ( k ) is the usual energy-spectrum function, β is the rate of enstrophy transfer per unit mass, C ′ is a dimensionless constant, and k 1 marks the bottom of the range, where enstrophy is pumped in. Transfer in the energy and enstrophy inertial ranges is computed according to an almost-Markovian Galilean-in variant turbulence model. Transfer in the two-dimensional energy inertial range, \[ E(k) = Cε2/3k-5/3, \] is found to be much less local than in three dimensions, with 60 % of the transfer coming from wave-number triads where the smallest wave-number is less than one-fifth the middle wave-number. The turbulence model yields the estimates C ′ = 2·626, C = 6·69 (two dimensions), C = 1·40 (three dimensions).