Ensemble model of turbulence based on states of constant flux in wavenumber space.

An ensemble model of turbulence is proposed. The ensemble consists of flow fields in which the flux of an inviscid conserved quantity, such as energy (or enstrophy in two-dimensional flow fields), across the wave number k is a constant independent of k in an appropriate range. Two-dimensional flow fields of constant enstrophy flux are sampled randomly by a Monte Carlo method. The energy spectra E_{k} of the flow fields are consistent with the scaling E_{k}∝k^{-3}[ln(k/k_{b})]^{-1/3} where k_{b} is the bottom wave number of the constant-flux range.