Intrinsic rotation of toroidally confined magnetohydrodynamics. Physical Review Letters, Accepted, preprint available hal.archives-ouvertes.fr/hal-00733093

The spatiotemporal self-organization of viscoresistive magnetohydrodynamics (MHD) in a toroidal geometry is studied: •The spontaneously generated flow changes from dominantly poloidal to dominantly toroidal. •Up-down asymmetry of the geometry is necessary to generate a non-zero net toroidal mass-flow. Background •Montgomery & Shan [1] and Bates & Lewis [2] investigated the case of visco-resistive MHD in toroidal geometry. They showed that, in the case of uniform resistivity and im-posed curl-free toroidal electric and magnetic fields, no static equilibria are possible, the magneto-fluid cannot remain quiescent. ∇ × (j×B) 6 = 0 = ⇒ ∇P 6 = j×B = ⇒ u 6 = 0. (1) Aims • The dynamics of the visco-resistive MHD equations in toroidal geometries are still largely unexplored. We therefore investigate the fully three-dimensional, non-stationary problem from low to moderate values of the Lundquist number. MHD equations and penalization method [4] • The dimensionless incompressible visco-resistive MHD equations including the penaliza-tion term (introduction of Dirichlet boundary conditions) in ‘Alfvénic ’ units, are ∂u ∂