Multifractal Analysis of Simulated Two-Dimensional Turbulence

Abstract

Simulated two-dimensional Navier-Stokes turbulence with the k -4 energy spectrum is considered from a multifractal point of view. The calculations cover the range of Reynolds numbers 55< R L <850. Turbulence has an inertial range in almost one decade of wave number. The generalized dimensions D q are computed for the enstrophy dissipation rate as well as the energy dissipation rate. For the former D ∞ =1.2∼1.3, implying that the intense enstrophy dissipation occurs nearly on a line. For the latter D q is close to two, the geometrical dimension, for positive values of q , which means that the energy dissipation occurs uniformly in space. We do not observe that both D q depend appreciablly on Reynolds number as well as the pattern of the initial large-scale fields. The pictures obtained from the multifractal considerations are consistent with what is known already in two-dimensional turbulence, implying that the multifractal analysis is a good tool for studying turbulence structure.