Conformations and persistence lengths of vortex filaments in homogeneous turbulence

Abstract

We propose a theory describing the conformations of the coherent vortex filaments observed in homogeneous and isotropic turbulence. These objects are pictured as a gas of non-interacting singular structures enveloped in a given background flow characterized by a self-similar energy spectrum. In a general way, we show that filament conformation can be mapped to a random walk problem with long-range correlations. Its Flory exponent is related to a correlation exponent within a self-consistent approximation, without invoking thermal equilibrium arguments. The filament fractal dimension and its energy spectrum also obey a simple relation. The filaments are locally linear and, at scales smaller than a persistence length, form rather straight lines. Under the assumption that these defects are special, intense realizations of the vorticity background statistics, we evaluate persistence lengths that show good agreement with previous simulation results at intermediate Reynolds numbers.