Nonlinear stability and the saturation of instabilities to axisymmetric vortices

Shepherd, T. G. ORCID: https://orcid.org/0000-0002-6631-9968 (1991) Nonlinear stability and the saturation of instabilities to axisymmetric vortices. European Journal of Mechanics & Fluids B: Fluids, 10 (2). pp. 93-98. ISSN 0997-7546

Abstract/Summary

Nonlinear stability theorems are presented for axisymmetric vortices under the restriction that the disturbance is independent of either the azimuthal or the axial coordinate. These stability theorems are then used, in both cases, to derive rigorous upper bounds on the saturation amplitudes of instabilities. Explicit examples of such bounds are worked out for some canonical profiles. The results establish a minimum order for the dependence of saturation amplitude on supercriticality, and are thereby suggestive as to the nature of the bifurcation at the stability threshold.