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. © 2013 IOP Publishing Ltd.

A novel mechanism for driving residual stress in tokamak plasmas based on k symmetry breaking by the turbulence intensity gradient is proposed. The physics of this mechanism is explained and its connection to the wave kinetic equation and the wave-momentum flux is described. Applications to the H-mode pedestal in particular to internal transport barriers, are discussed. Also, the effect of heat transport on the momentum flux is discussed. © 2010 American Institute of Physics.

A simple model for the evolution of turbulence fluctuation spectra, which includes neighboring interactions leading to the usual dual cascade as well as disparate scale interactions corresponding to refraction by large scale structures, is derived. The model recovers the usual Kraichnan-Kolmogorov picture in the case of exclusively local interactions and midrange drive. On the other hand, when disparate scale interactions are dominant, a simple spectrum for the density fluctuations of the form |nk|2 proportional to k(-3)/(1+k2)2 is obtained. This simple prediction is then compared to, and found to be in fair agreement with, Tore Supra CO2 laser scattering data.

Simple flux-gradient relations that involve time delay and radial coupling are discussed. Such a formulation leads to a rather simple description of avalanches and may explain breaking of gyroBohm transport scaling. The generalization of the flux-gradient relation (i.e., constitutive relation), which involve both time delay and spatial coupling, is derived from drift-kinetic equation, leading to kinetic definitions of constitutive elements such as the flux of radial heat flux. This allows numerical simulations to compute these cubic quantities directly. The formulation introduced here can be viewed as an extension of turbulence spreading to include the effect of spreading of cross-phase as well as turbulence intensity, combined in such a way to give the flux. The link between turbulence spreading and entropy production is highlighted. An extension of this formulation to general quasi-linear theory for the distribution function in the phase space of radial position and parallel velocity is also discussed.

Turbulence in hot magnetized plasmas is shown to generate permeable localized transport barriers that globally organize into the so-called "ExB staircase" [G. Dif-Pradalier et al., Phys. Rev. E, 82, 025401(R) (2010)]. Its domain of existence and dependence with key plasma parameters is discussed theoretically. Based on these predictions, staircases are observed experimentally in the Tore Supra tokamak by means of high-resolution fast-sweeping X-mode reflectometry. This observation strongly emphasizes the critical role of mesoscale self-organization in plasma turbulence and may have far-reaching consequences for turbulent transport models and their validation.