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Nonlinear parallel momentum transport in strong turbulence

Most existing theoretical studies of momentum transport focus on calculating the Reynolds stress based on quasilinear theory, without considering the \emph{nonlinear} momentum flux-$<\tilde{v}_r \tilde{n} \tilde{u}_{\|} >$. However, a recent experiment on TORPEX found that the nonlinear toroidal momentum flux induced by blobs makes a significant contribution as compared to the Reynolds stress [Labit et al., Phys. Plasmas {\bf 18}, 032308 (2011)]. In this work, the nonlinear parallel momentum flux in strong turbulence is calculated by using three dimensional Hasegawa-Mima equation. It is shown that nonlinear diffusivity is smaller than quasilinear diffusivity from Reynolds stress. However, the leading order nonlinear residual stress can be comparable to the quasilinear residual stress, and so could be important to intrinsic rotation in tokamak edge plasmas. A key difference from the quasilinear residual stress is that parallel fluctuation spectrum asymmetry is not required for nonlinear residual stress.