The direct-current plasma arc is the principal heating and stirring element in plasma arc furnaces. The arc is a highly dynamic system operating at very short time scales (milliseconds or less). This dynamic behaviour can be understood as the combination of several modes of instability acting together. These modes can include fluid dynamic/shear layer instabilities, near-electrode instabilities resulting from steep local temperature gradients and other electrode surface effects, or helical/twisting instabilities resulting from the magnetic field generated in one part of the arc column exerting a force on another. Computational magneto-hydrodynamic models of the arc which are able to reproduce the highly transient behaviour of the system are developed to study certain dynamic modes - in particular, the formation and evolution of axisymmetric vortices and shear layer instabilities in the arc jet. Results from this work are then compared to qualitative data from high-speed photographic imaging of large plasma arcs (up to 3 kA current). (C) 2013 Elsevier Ltd. All rights reserved.