Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an orthonormal frame attached to each Lagrangian fluid particle undergoing three-axis rotations, by using quaternions in combination with Ertel's theorem for frozen-in vo...

The paper considers the plane one-dimensional flows for magnetohydrodynamics in mass Lagrangian coordinates. inviscid, thermally non-conducting medium is modeled by a polytropic gas. equations are examined symmetries and conservation laws. For case of finite electric conductivity we establish Lie group classification, i.e. describe all cases $ \sigma ( \rho , p)$ which there symmetry extensions...

This Letter discusses the role of a weak toroidal magnetic field in modifying the turbulent transport properties of stably stratified rotating turbulence in the tachocline. A local two-dimensional b-plane model is investigated numerically. In the absence of magnetic fields, nonlinear interactions of Rossby waves lead to the formation of strong mean zonal flows. However, the addition of even a v...