On the optimal vorticity function of vortex rings

Abstract

We present here an original approach to reconstruct the vorticity distribution inside an axisymmetric vortex ring from some incomplete and possibly noisy measurements of the corresponding velocity field. The idea is to formulate an inverse problem for identifying the structure of the vorticity distribution and solve this problem by a suitable numerical optimization algorithm. The novelty of the present study is that the vorticity function is reconstructed in a very general form with no assumptions other than smoothness and the behaviour at the endpoints of its domain of definition. This is fundamentally different from classical approaches reducing the reconstruction problem to fitting a small number of variables parameterizing the vorticity distribution of a given vortex-ring model.