The swirling flow exiting the runner of a hydraulic turbine is further decelerated in the discharge cone of the draft tube to convert the excess of dynamic pressure into static pressure. When the turbine is operated far from the best efficiency regime, particularly at part load, the decelerated swirling flow develops a self-induced instability with a precessing helical vortex, with associated severe pressure fluctuations. This phenomenon is investigated numerically in this paper, for a swirl apparatus configuration. The unsteady three-dimensional flow field is analyzed using a proper orthogonal decomposition (POD), and within this framework we examine the effectiveness of an axial jet injection for mitigating the flow instability. It is shown that a limited number of modes can be used to reconstruct the flow field. Moreover, POD enables to reveal influence of the jet injection on the individual modes of the flow and illustrates continuous suppression of the modes from higher order modes to lower order modes as the jet discharge increases. Application of POD offers new view for the future control effort aimed on vortex rope mitigation, because spatio-temporal description of the flow is provided. Thereby POD enables better focus of the jets or other flow control devices.