In this paper, the criterion on nonlinear stability of swirling jet flow is theoretically obtained based on the assumption that the high-order perturbation is kept in the perturbation equation of momentum. The nonlinear stability frequency curves of different points of jet at the initial time are got by numerical computation for the first time. Several conclusions on nonlinear stability of swirling jet flow are detailedly presented founded on analysis and comparison of the obtained nonlinear stability frequency curves as well as the existent linear one. The most important among them is that the equation controlling nonlinear stability of swirling jet flow at the initial time degenerates from a two-order algebraic equation to a one-order one for some relatively large wavenumbers.
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