Modelling of turbulence driven momentum tranport

We suggest a simple model of turbulence driven transport of parallel momentum. The model incorporates the commonly invoked effects of diffusion, so-called momentum ``pinch'' term (i.e. a supposedly inward advection of mean momentum) and an additional off-diagonal term driven by and proportional to the radial $\mathbf{E\times B}$ shear. It is observed that in a cylinder the a part of this ``pinch'' term comes from the fact that particles can carry momentum, and that there is a pinch in particle transport. On the other hand, the off-diagonal term comes purely from the Reynolds stress between the parallel momentum fluctuations and the perpendicular $\mathbf{E\times B}$ fluctuations, and it requires symmetry breaking. The form of the model presented here is based on the assumption that the dominant mechanism for symmetry breaking in the core of a periodic cylinder is a shift of the eigenmode from the rational surface induced by the radially sheared poloidal $\mathbf{E\times B}$ flow.