Decay of a Potential Vortex. Fractional Model

Abstract

Decay of a potential vortex through an incompressible viscous fluid is numerically studied using a fractional model. The influence of temporal and spatial fractional parameters on the fluid velocity and the circulation on a circle of radius r is graphically represented and discussed. As the corresponding diagrams are almost identical and difficult enough to be distinguished, five tables with numerical values have been included. The differences are small enough, but they exist. In all cases the vortex deaden in space. As a check of results that have been obtained, a comparison between numerical and exact solutions is presented. As expected, when the fractional parameters are in close proximity of one and the third parameter δ tends to one, the velocity profiles corresponding to the numerical solution tends to superpose over that of exact solution.