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An experimental and CFD study is presented of the flow with shock waves from vertical plasma breakdown column 24 mm long. High specific energy input of pulse discharge with plasma electrodes in the discharge camera was evaluated trough comparison of CFD results and high-speed shadowgraphy. Cylindrical shock waves arising from the energy input based on the vertical breakdown were visualized. Flow evolution up to 3 ms after discharge was studied with high-speed shadowgraphy. Speed and intensity of shock waves were measured; also instability of hot post-discharge channel was visualized. A 2D numerical simulation of the initiation of shock-wave flows based on the Navier-Stokes equations was made. The model of pulse cylindrical energy deposition was used, based on experimental data. Solving the inverse problem shows that 20-22% of the energy of the volume discharge, stored in the capacitor is converted into energy of cylindrical shock waves - in the vertical breakdown channel. In the presence of low density area (vortex column) in gas flow the controlled breakdown (self-localization of the discharge plasma) occurs. Images of plasma glow localization in flow with vortexes were obtained.