  We consider the incompressible 2D Euler equation in an infinite cylinder
$\mathbb{R}\times \mathbb{T}$ in the case when the initial vorticity is
non-negative, bounded, and compactly supported. We study $d(t)$, the diameter
of the support of vorticity, and prove that it allows the following bound:
$d(t)\leq Ct^{1/3}\log^2 t$ when $t\rightarrow\infty$.
