Conformations and persistence lengths of vortex filaments in homogeneous turbulence

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