The spiral wind-up and dissipation of vorticity and a passive scalar in a strained planar vortex

The response of a Gaussian vortex to a weak time-dependent external strain field is studied numerically. The cases of an impulsive strain, an on-off s tep function, and a continuous random strain are considered. Transfers of e nstrophy between mean and azimuthal components are observed, and the result s are compared with an analogous passive scalar model and with Kida's ellip tical vortex model. A 'rebound' phenomenon is seen: after enstrophy is transferred from mean to azimuthal component by the external straining field, there is a subsequent transfer of enstrophy back from the azimuthal component to the mean. Analy tical support is given for this phenomenon using Lundgren's asymptotic form ulation of the spiral wind-up of vorticity. Finally the decay of the vortex under a continuous random external strain is studied numerically and compa red with the passive scaler model. The vorticity distribution decays more s lowly than the scalar because of the rebound phenomenon.