Wavy Magnetohydrodynamic Turbulence

Nonlinear closure models of the 2D magnetohydrodynamic equations predict that the turbulent diffusivity of magnetic fields in high magnetic Reynolds number flows will be strongly suppressed below the value predicted by simple kinematic models.

The consequences of such 'resistivity quenching' for models of dissipation and transport in magnetized flows are profound.

However, to date, there has been little examination of the underlying assumptions implicitly made by such models---(i) that the quenching is associated with a reduction in the cross-phase between the velocity and the magnetic potential, rather than a suppression of the turbulence itself, and (ii) that transport results from molecular collisions alone.

In this dissertation, we revisit the 2D problem in an attempt to address these issues.

To address (i), we examine the normalized cross-phase and its dependence on the initial magnetic field strength.

We present the results of numerical simulations that are consistent with the current picture of resistivity quenching as primarily a suppression of transport of magnetic potential rather than turbulence intensity.

To address (ii), the theory of turbulent resistivity in 'wavy' magnetohydrodynamic turbulence in 2D is presented.

The goal is to explore the theory of resistivity quenching in a regime for which the mean-field theory can be rigorously constructed at large magnetic Reynolds number Rm .

This is achieved by extending the simple 2D problem to include body forces, such as buoyancy or the Coriolis force, that convert large scale eddies into weakly interacting dispersive waves.

Remarkably, adding an additional restoring force to the already tightly constrained system of high Rm magnetohydrodynamic turbulence in 2D can actually increase the turbulent resistivity, by admitting a spatial flux of magnetic potential, driven by wave interactions, that is not quenched at large Rm.

In the final chapter we address a closely related topic: the effect of magnetic linkage on the homogenization of vorticity in closed streamline flow.

It is found that magnetic stresses acting on the bounding streamline can maintain a cross-stream gradient in the vorticity, thus disrupting the homogenization process and profoundly altering the nature of the turbulent enstrophy cascade in such flows.