How Vortices Mix

The advection of a passive scalar blob in the deformation field of an axisymmetric vortex is a simple mixing protocol for which the advection-diffusion problem is amenable to a near-exact description. The blob rolls up in a spiral which ultimately fades away in the diluting medium. The complete transient concentration field in the spiral is accessible from the Fourier equations in a properly chosen frame. The concentration histogram of the scalar wrapped in the spiral presents unexpected singular transient features and its long time properties are discussed in connection with real mixtures