Tangled magnetic fields, often coexisting with an ordered mean field, have a major impact on turbulence and momentum transport in many plasmas, including those found in the solar tachocline and magnetic confinement devices. In this dissertation, we present research on the turbulent transport in presence of a stochastic magnetic field, and the discuss implications on the formation of astronomical objects and on the turbulence in edge plasma in fusion devices.

The research is divided into three projects. First, we present a novel mean field theory of potential vorticity mixing in β -plane magnetohydrodynamic (MHD). Our results show that mean square stochastic fields strongly reduce Reynolds stress coherence. This decoherence of potential vorticity flux due to stochastic field scattering leads to suppression of momentum transport and zonal flow formation. We discuss a model of stochastic fields as a resisto-elastic network.

In second project, we shows the breaking of the shear-eddy tilting feedback loop by stochastic fields is the key underlying physics mechanism. A simple calculation suggests that the breaking of the shear-eddy tilting feedback loop by stochastic fields is the key underlying physics mechanism. A dimensionless parameter that quantifies the increment in power threshold is identified and used to assess the impact of stochastic field on the L-H transition in fusion devices.

Finally, we study the turbulent transport of parallel momentum and ion heat by the interaction of stochastic magnetic fields and turbulence in third project. Attention is focused on determining the kinetic stress and the compressive energy flux. A critical parameter is identified as the ratio of the turbulent scattering rate to the rate of parallel acoustic dispersion. For the parameter large, the kinetic stress takes the form of a viscous stress. For the parameter small, the quasilinear residual stress is recovered. In practice, the viscous stress is the relevant form, and the quasilinear limit is not observable. This is the principal prediction of this project.