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Steady solutions to the governing equations that describe fully two-dimensional arc plasmas in a plug flow have been obtained. The stability of these steady solutions is investigated by calculating the transient created when infinitesmal changes in the electrode potentials are imposed. Comparisons are made with solutions obtained using a one-dimensional electric field. We find that with increasing blowing (Peclet number) the one-dimensional electric field solutions yield increasingly inaccurate results for higher currents. The stability results conform with those given by the classical Kaufmann criterion. We find that convection tends to reduce and eventually to eliminate the declining branch of the current-voltage characteristic. The presence of convection promotes axial temperature gradients in the arc and hastens the transition from the unstable (declining) branch to a stable (increasing) branch of the current-voltage characteristic.