In this thesis we consider turbulent fluid systems. We develop a closure scheme in which the mean velocity field of an incompressible fluid is driven by a turbulent velocity field possessing a non-zero mean helicity. We use this to investigate the formation of large scale vortices and the behaviour of the mean kinetic energy, enstrophy and helicity. The same technique is then applied to the equations of magneto-hydrodynamics, in order to explain the self-generation of mean magnetic fields, and the joint formation of current and vortex structures. We then discuss the convection of a passive scalar by the fluid and determine an equation for the mean temperature. Finally we present a theory to account for the behaviour of a two-dimensional electrically conducting fluid subject to a constant external magnetic field driven by external forces. We explain the peaks in the power spectrum, the saturation of the magnetic and kinetic energies, and the insensitiveness of their equilibrium value on the external field. All of these are observed in numerical experiments.

This thesis presents an improved feedback system on HBT-EP and suppression of the fast rotating kink mode using this system. HBT-EP is an experimental tokamak at Columbia University designed to study the magnetohydrodynamic (MHD) instabilities in confined fusion. The most damaging instabilities are global long wavelength kink modes, which break the toroidal symmetry of the magnetic structure and lead to plasma disruption and termination. When a tokamak is surrounded by a close fitting conducting wall, then the single helicity linear dispersion relation of the kink instability has two ominating branches: one is the "slow mode", rotating at the time scale of wall time, known as resistive wall mode (RWM), the other is the fast mode, that becomes unstable near the ideal wall stability limit. Both instabilities are required to be controlled by the feedback system in HBT-EP. In this thesis, improvements have been made upon the previous GPU-based system to enhance the feedback performance and obtain clear evidence of the feedback suppression effect. Specifically, a new algorithm is implemented that maintains an accurate phase shift between the applied perturbation and the unstable mode. This prevents the excitation of the slow kink mode observed in previous studies and results in high gain suppression for fast mode control at all frequency for the first time. When the system is turned off, suppression is lost and the fast mode is observed to grow back. The feedback performance is tested with several wall configurations including the presence of ferritic material. This provides the first comparison of feedback control between the ferritic and stainless wall. The effect of plasma rotation on feedback control is tested by applying a static voltage on a bias probe. As the mode rotation being slowed by the radial current flow, a higher gain on the kink mode is required to achieve feedback suppression. The change in plasma rotation also modifies the plasma response to the external perturbation. The optimal phase shift for suppression changes with the modified response and these observations are consistent with the predictions of the single helicity model.