A general theory of curved vortices with circular cross-section and variable core area

A theory is derived for general motions of an inviscid vortex with circular crosssection and variable core area using a directed filament model of the vortex. The theory reduces in special cases to any of several previous vortex theories in the literature, but it is better suited than previous theories for handling nonlinear areavarying waves on the vortex core. Jump conditions across points of discontinuity and a variational form of the theory are also given. The theory is applied to obtain new solutions for several fundamental problems in vortex dynamics related to axisymmetric solitary waves on a vortex core, axisymmetric and helical vortex breakdowns and the buckling of a columnar vortex under compression.

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