One-particle two-time diffusion in three-dimensional homogeneous isotropic turbulence

A model of turbulence based on a summation of Fourier modes with an imposed turbulent energy spectrum, E ( k ) ∼ k − p , is used to investigate the characteristics of one-particle diffusion in turbulent flow. The model is described and the general Eulerian field is investigated. Using a number of Lagrangian statistical measures the results from the model are compared with laboratory experiments [N. Mordant, P. Metz, O. Michel, and J.-F. Pinton, “Measurement of Lagrangian velocity in fully developed turbulence,” Phys. Rev. Lett. 87, 214501 (2001)]. The correlation structure and spectral properties of the real and modeled fields agree well under certain time dependency conditions. The correlation signature of Lagrangian accelerations is shown to reflect the persistence of the underlying streamline structure. Intermittency may influence these correlations but is not their primary cause.