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Arakel Petrosyan, Space Research Institute, Moscou, Russie

Shallow Water Magnetohydrodynamics in Rotating Flows. Waves, Turbulence and Zonal Flows.

Vendredi 25 janvier 2019, 11h, ECL, amphi 203

Shallow Water Magnetohydrodynamics in Rotating Flows. Waves, Turbulence and Zonal Flows.

A number of new applications in astrophysics and recent space observations actualized the problem of study and description of rotating magnetohydrodynamic fluid behavior. In presentation I review recent achievements in studies of large-scale magnetohydrodynamic flows in rotating frame. We focus on magnetohydrodynamic shallow water approximation for rotating plasma and on two-dimensional magnetohydrodynamic flows on a beta plane. The MHD shallow-water equations in presence of rotation with an external magnetic field are revised by supplementing them with the equations that are derived from magnetic field divergence-free condition. New system reveals the existence of the third component of magnetic field in this approximation and provides relation with the horizontal magnetic field. The presence of a vertical magnetic field significantly changes the dynamics of wave processes in astrophysical plasma compared to the neutral fluid and plasma layer in a horizontal magnetic field. The shallow-water approximation has been used for the development of the weakly nonlinear theory of magneto-Poincare and magneto-Rossby waves both in external vertical magnetic field and in the absence of magnetic field, as well as for stationary states in the presence of a horizontal field (poloidal, toroidal, and their sum). Qualitative analysis of the dispersion curves for the Poincare and Rossby waves in magnetohydrodynamics revealed the possibility of three-wave interactions in the weak nonlinearity approximation. The weakly nonlinear theory of magneto-Rossby waves developed using the method of multiscale asymptotic expansions and three-wave equations for slowly varying amplitudes are briefly outlined. Approximate analysis of the resultant systems of equations has revealed that two types of parametric instability can evolve in the system: parametric decay and parametric amplification of magneto-Poincare and magneto-Rossby waves. The first results of numerical simulation of two-dimensional decaying MHD turbulence on the betta plane are discussed. Numerical simulations demonstrate the formation of zonal flows in MHD turbulence on the betta plane. Zonal flows in MHD turbulence on the betta plane significantly differs from flows in the neutral fluid. Zonal flows in MHD turbulence are unsteady because of the presence of isotropic magnetic islands in the system. The inverse energy cascade in decaying MD turbulence on the betta-plane terminates at the scale that differs from the Rhines scale but is consistent with our new criterion of the boundary between wave dynamics and MHD turbulence.


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