Dynamics of tilted eddies in a transversal flow at the edge of tokamak plasmas and the consequences for L-H transition

The dynamical interaction between eddies and shear flow is investigated through a simplified model of vorticity conservation with tilted eddies. Energy is transferred either to the flow or to eddies, depending on the eddy tilt with respect to the flow shear. When eddies are tilted in the shear direction, the system is favorable to shear increase: tilt instability (TI) or the negative viscosity phenomenon. When eddies are tilted in the opposite direction, the shear flow is damped via a Kelvin-Helmholtz (KH) process. The TI generally dominates the interaction on the largest radial scale, but a fraction of the energy cascades to smaller radial scales through the alternation of tilting and KH dynamics. Within this eddy description, we show that the symmetry breaking required to generate a net residual stress is set by the intrinsic eddy tilt. We recall that magnetic shear can provide an intrinsic tilt to ballooning modes at the edge of tokamak plasmas, with an orientation which depends on flux surface geometry. In L-mode weak shear regimes, this residual stress can dominate the Reynolds stress. Coupled to momentum sources acting in the scrape-off layer, it can induce a significant difference of the edge radial electric field between lower single null and upper single null geometries. A comparison with experimental profiles measured across the edge of Tore Supra L-mode plasmas is discussed.