Open Access Publications from the University of California

## Topics in Mesoscopic Turbulent Transport

• Author(s): Heinonen, Robin
The self-propagation of turbulence, called turbulence spreading,'' can lead to turbulence invading linearly stable regions of a tokamak. In the second project, we introduce a new model for turbulence spreading based on turbulence bistability. This model takes the form a reaction-diffusion equation with cubic nonlinearity and nonlinear diffusion. We find that the bistable model remedies certain deficiencies of the popular, unistable Fisher model, for instance predicting far more robust penetration of turbulence into stable regions. We also find that the model exhibits a threshold for propagation of an initial seed of turbulence, which we liken to an avalanche. We analytically estimate this threshold using a simple physical argument.
Finally, we study momentum transport in magnetohydrodynamic (MHD) turbulence on a $\beta$-plane, which serves as a simple model for the solar tachocline. We show that the cross-helicity, which is conserved in pure MHD turbulence, builds up to a predictable level in this system. Using weak turbulence theory, we also show that the cross helicity spectrum is equivalent to the Els\"asser alignment spectrum, which determines momentum transport. We supplement and verify our results with direct numerical simulations.