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Topics in Mesoscopic Turbulent Transport

  • Author(s): Heinonen, Robin
  • Advisor(s): Diamond, Patrick H
  • et al.
Abstract

The interaction of turbulent microscales in a plasma can conspire to produce transport on mesoscopic or macroscopic scales, often with extremely important consequences for the system. In this dissertation, we present research on mesoscopic turbulent transport in plasmas relevant to fusion energy and astrophysics.

The research is divided into three projects. First, we study drift-wave turbulence, a paradigm for gradient-driven turbulence in the tokamak, using a novel data-driven method. Deep learning is used to infer, from direct numerical simulation of the 2-D Hasegawa-Wakatani system, the dependencies of the turbulent fluxes which control the nonlinear dynamics on mesoscales, thus closing a simplified 1-D mean-field model. Using this approach, we show that the gradient of vorticity drives a nondiffusive particle flux. This nondiffusive flux, which we also recover analytically, modulates the profile in the presence of a quasiperiodic zonal flow. We also show that zonal flow formation is described by a Cahn-Hilliard-type model, both concurring with and expanding upon previous theoretical work.

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.

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