In a recent paper Ducharme et al presented a model for a free-burning tungsten inert gas (TIG) electric arc with non-consumable electrodes using a flat anode and argon shielding gas. The model evaluates the laminar gas flow, temperature distribution and electric field in the arc column by treating the current carrying region of the arc as a partially ionized plasma in local thermodynamic equilibrium. The dependence of transport coefficients on temperature is taken into account, as is the entrained shielding gas flow entering the arc from around the cathode. This model is extended here to investigate both 5 mm long 200 A and 10 mm long 100 A electric arcs at elevated pressures in the ranges 1 - 5 and 1 - 14.8 bar respectively. The results of the electric arc model are found to be in satisfactory agreement with a range of experimental data including spectroscopic temperature maps, electric field distributions, voltage drops, arc radii and total radiative emissions. It has been shown by Allum et al that short arcs length < 4 mm) become unstable once a critical Reynolds number has been reached, signifying the onset of turbulence for the flow emerging from the arc nozzle. This analysis, however, does not explain the inherent instability of longer arcs, which may be present even in a still argon atmosphere. It is proposed here that these are caused by the onset of turbulence in the entrained shielding gas. Two seperate Reynolds numbers, therefore, come into play in the physics of the TIG arc in connection with instabilities and these are estimated in the paper.