Lagrangian structure function and spectrum of a two-dimensional turbulent flow

An analysis of the relationship between the Lagrangian energy spectrum and the second-order structure function of a two-dimensional, incompressible, steady turbulent flow is presented. It is shown that the structure function is practically independent of the Lagrangian spectral slope as soon as the latter is nonlocal. The analysis, together with results from Babiano et al. (1984) and Middleton (1984), leads to a principle of indeterminacy for the energy spectrum in the nonlocal case which is valid for both Lagrangian and Eulerian spectra. The structure function obtained in a numerical simulation of two-dimensional turbulence, as well as the evolution of single-particle dispersion are illustrated.