Locality properties of the energy flux in turbulence

The scale locality functions, originally introduced by Kraichnan, are computed from results of direct numerical simulations of forced isotropic turbulence. It is found that a curve with the classical, asymptotic scaling exponent of 4/3 provides the lower bound for the numerical data in the infrared limit and the upper bound in the ultraviolet limit, i.e., the nonlocality effects are stronger in the infrared and weaker in the ultraviolet than the theoretical result obtained for an infinite inertial range. The departures from the 4/3 scaling are substantial for fully resolved direct numerical simulations at lower Reynolds number but decrease for forced simulations that impose the −5/3 spectrum outside the energy containing range.