The authors have obtained sufficient conditions for the nonlinear stability of incompressible, inviscid, swirling flows using the Arnol’d energy-Casimir method. Equations of motion in swirling function-vortex- density form have been used and an axisymmetric Lie-Poisson bracket has been derived. The flows and perturbations considered have axial variations only. The formulation is analogous to that of two-dimensional, stratified Boussinesq flows discussed by H. D. I. Abarbanel, D. D. Holm, J. E. Marsden and T. S. Ratiu [Philos. Trans. R. Soc. Lond., A 318, 349-409 (1986; Zbl 0637.76119)]. Several examples of columnar swirling flows have been discussed and relation to linear stability theory of swirling flows is established.