A new approach to studying the dynamics of a thin curved vortex

The paper studies the dynamics of a thin curved vortex in a potential flow of an ideal incompressible fluid. The flow is specified by a number of geometrical restrictions and does not satisfy the Biot–Savart law. The form of the derived equation of the vortex dynamics coincides with the form of the well-known equation of local induction for self-induced vortex motion. The parameters of the new equation are simultaneously flow parameters, and in this sense, they do not show uncertainty typical of classical equations. The coefficient of the new equation can take any specified values (not necessarily much greater than unity, as required according to the concept of local induction) and generally is a function of a natural filament parameter.