On the application of nonextensive statistics to Lagrangian turbulence

A second-order Lagrangian stochastic model formulated in terms of the mean dissipation rate and satisfying the well-mixed condition for a Tsallis distribution of Lagrangian accelerations is shown to be incompatible with Kolmogorov’s similarity theory. This difficulty does not arise when, following the approach advocated by Beck [Phys. Rev. Lett. 87, 180601 (2001)], the Tsallis distribution is recovered from a Gaussian model through the employment of a distribution of dissipation rates. The effects caused by ignoring fluctuations in dissipation along trajectories are evaluated in numerical simulations in which Lagrangian accelerations and dissipation histories evolve jointly as a Markovian process.