  We give an example of a weakly mixing vector field $b\in
L^\infty([0,1],\text{BV}(\mathbb{T}^2))$ which is not strongly mixing. The
example is based on a work of Chacon who constructed a weakly mixing
automorphism which is not strongly mixing on
$([0,1],\mathcal{B}([0,1]),|\cdot|)$, where $\mathcal{B}([0,1])$ are the Borel
subsets of $[0,1]$ and $|\cdot|$ is the one-dimensional Lebesgue measure.
