Numerics and experiments of nonlinear MHD waves in differentially rotating spherical geometry

An overview of the nonlinear dynamics of the magnetised spherical Couette flow is presented. This problem is fundamental for understanding magnetohydrodynamic MHD instabilities occurring when a liquid metal flow, driven by the rotation of the inner boundary in a spherical shell, is subjected to an axial magnetic field. The analysis, at a moderate rotation rate and applied magnetic fields, is based on direct numerical simulations and numerical tools from dynamical systems and chaos theory, as well as laboratory experiments. Several type of MHD waves are classified and a reasonable agreement between simulations and experiments is obtained.