The article presents the theoretical research of the use of swirling flows with reverse jets and with developed precessing vortex core in cavitators and other devices. While describing the motion of the vortex core in the free swirling jet of the fluid it is necessary to take into account that according to the experimental data the vortex core can swirl along the length of the jet and moves around the jet axis in the zone between the area of reverse flows and the boundary outer layer. In this case, it is the vortex core which is under the influence of the basic swirling flow. Herewith, it is necessary to take into account that due to commensurate sizes of the vortex core and the jet, the impact on the core will be different owing to non-uniform distribution of speeds in the jet itself. On the basis of the known formulas, the authors have deduced the improved theoretical dependence of the degree of flow swirl on the flow rate, the vortex core vibration frequency and structural parameters under the conditions of the consistency of swirling flow itself. The theoretical dependence shows that the degree of flow swirl is directly proportional to the precessing vortex core vibration frequency and inversely proportional to the square of mass flow rate. Thus, ensuring the consistency of the swirling flow with varying flow-rate requires the corresponding change of the swirl degree or the influence on the frequency of vibrations of the precessing vortex core. On the basis of the deduced theoretical dependences, the authors have developed and implemented in the computer programs the following calculations: the dependence of the coefficient of the flow swirl on the vortex core vibration frequency; the simulation of the precession of the vortex core in the swirling flow; the research of speed fluctuation in the swirling flow; speed fluctuation during the interaction of swirling jets