Lagrangian evolution of velocity increments in rotating turbulence: the effects of rotation on non-Gaussian statistics

The effects of rotation on the evolution of non-Gaussian statistics of velocity increments in rotating turbulence are studied in this paper. Following the Lagrangian evolution of the velocity increments over a fixed distance on an evolving material element, we derive a set of equations for the increments, which provides closed representation for the nonlinear interaction between the increments and the Coriolis force. Applying a restricted-Euler-type closure to the system, we obtain a system of ordinary differential equations, which retains the effects of nonlinear interaction between the velocity increments and the Coriolis force. A-priori tests using direct numerical simulation data show that the system captures important dynamics of rotating turbulence. The system is integrated numerically starting from Gaussian initial data. It is shown that the system reproduces qualitatively a number of observations in rotating turbulence. The statistics of the velocity increments tend to Gaussian when strong rotation is imposed. The negative skewness in the longitudinal velocity increments is weakened by rotation. The model also predicts that the transverse velocity increment in the plane perpendicular to the rotation axis will have positive skewness, and that the skewness will depend on the Rossby number in a non-monotonic way. Based on the system, we identify the dynamical mechanisms leading to the observations.