Insight into singular vortex flows

Abstract

The method of three-dimensional vortex singularities is analyzed. The fact that it does not represent a weak solution of the Euler equations has little bearing on its validity as an operative model. Other evolution inconsistencies are a major problem. The non-solenoidality of the vortex field is analyzed and a linear filtering feedback procedure, requiring no additional computations, is introduced to allow alignment with the reconstructed solenoidal vorticity field. A rough estimation of the dissipative effect during vortex reconnection has shown a finite viscous effect that is implicitly present in the model, growing with stretching, representing the mechanism of shifting to reconnected topologies without observing strong velocity gradients. The dividing vorton method is rearranged in order to allow the quantized reproduction of a predefined core evolution law, an error estimation, due to the corpuscularity of the field, is given. Two different numerical computations are performed corresponding to a weak and a strong vortex interaction. The improvements are tested, and confrontations with existing numerical and experimental results are performed showing good agreement. The possibility of the singular vortex flow serving as a rough, but simple, model for very high Reynolds number complex flows is discussed.