Processes in the worldwide unique type of thermal plasma generator with water vortex stabilization and combined stabilization of arc by argon flow and water vortex have been numerically studied. Two-dimensional axisymmetric numerical model assumes laminar and compressible plasma flow in the state of local thermodynamic equilibrium. The calculation domain includes the arc discharge area between the near-cathode region and the outlet nozzle of the plasma torch. Radiation losses from the arc are calculated by the partial characteristics method for atmospheric pressure water and argon-water discharges. Thermal, electrical and fluid-dynamic characteristics of such arcs have been studied for the range of currents 150÷600 A under the assumption that radiation losses and plasma density depend linearly on pressure. It was proved that, taking this dependence into account, plasma velocity decrease while power losses from the arc by radiation and radial conduction increase with current. Outlet plasma temperature as well as electric potential drop remain practically unchanged.PACS : 52.25.Jm