  We study the mixing properties of a scalar $\rho$ advected by a certain
incompressible velocity field $u$ on the two dimensional unit ball, which is a
stationary radial solution of the Euler equation. The scalar $\rho$ solves the
continuity equation with velocity field $u$ and we can measure the degree of
mixedness of~$\rho$ with two different scales commonly used in this setting,
namely the geometric and the functional mixing scale. We develop a physical
space approach well adapted for the quantitative analysis of the decay in time
of the geometric mixing scale, which turns out to be polynomial for a large
class of initial data. This extends previous results for the functional mixing
scale, based on the explicit expression for the solution in Fourier variable,
results that are also partially recovered by our approach.
