Rotational dynamics of turbulence and Tsallis statistics

Abstract

The Langevin equation and its adaptations can reproduce accurately key aspects of fluid-particle motions in turbulent flows including: ballistic and normal-diffusive transport regimes, Lagrangian velocity autocorrelation functions and integral Lagrangian timescales. More recently it has become apparent that trajectory-rotations are also important dynamical quantities and that non-zero mean rotations are associated with suppressed rates of turbulent dispersion and oscillatory Lagrangian velocity autocorrelation functions. Here, it is shown that rotations of the Lagrangian velocity vector produced by the simplest and most widely used of such models coincide closely with the intense rotations measured in the recent seminal experiment by Zeff et al. [Nature 421 (2003) 146] and are described precisely by Tsallis statistics. Model predictions (Tsallis distributions) for the rotational statistics of the North Atlantic Ocean (region between 35–43 °W and between 36–42 °N) are found to be in close agreement with simulation data produced by the Miami Isopycnic-Coordinate Ocean Model.