Dispersion of passive tracers in the direct enstrophy cascade: Experimental observations

Abstract

The paper reports a statistical analysis of the separation of pairs in the enstrophy cascade, in a two-dimensional flow. The flow is produced experimentally, using electromagnetic forcing. Two regimes of separation are found. At early times (i.e., within two integral times) the separation process is exponential, following Lin’s law [J. T. Lin, J. Atmos. Sci. 29, 394 (1972)]. In this range of time, the probability density functions (PDFs) of separations are self-similar in time, developing stretched exponential tails, and one may define a Lagrangian correlation time. Above two integral times, an algebraic regime takes place, with exponential tails for the PDFs of the separations, and self-similar Lagrangian correlation functions. The present work thus confirms the existence of two regimes, by analyzing a number of statistical quantities including the Lagrangian PDF and the temporal Lagrangian correlation functions which so far, were left undetermined for the Batchelor regime.