Small-scale intermittency and local anisotropy in turbulent mixing with rotation

Abstract

The statistics of the velocity and passive scalar gradients in rotating turbulence are studied using Lagrangian stochastic models. Models for the velocity gradients are derived generalizing the approach proposed by Chevillard and Meneveau (Lagrangian dynamics and statistical geometric structure of turbulence, Phys. Rev. Lett. 97 (2006), p. 174501), whereas the scalar gradients are described using the model proposed by Gonzalez (Kinematic properties of passive scalar gradient predicted by a stochastic Lagrangian model, Phys. Fluids 21 (2009), p. 055104). The non-Gaussian and anisotropic statistics of the gradients are analyzed, and compared with available results in the literature. It is found that the models reproduce the observation that rotation tends to reduce small-scale intermittency for both velocity and scalar gradients. The models predict the skewness of the transverse velocity gradient components in the perpendicular plane and its non-monotonic dependence on the rotation rate. The models also reproduce the anisotropy in the scalar gradient at intermediate Rossby numbers. Furthermore, we show that the anisotropy is reached at an intermediate rotation rate, and the maximum coincides with a transition in the relative importance of the self- and cross-production terms for the scalar gradient.