  We prove linear in time filamentation for perturbations of the Lamb dipole,
which is a traveling wave solution to the incompressible Euler equations in
$\mathbb{R}^2$. The main ingredient is a recent nonlinear orbital stability
result by Abe-Choi. As a consequence, we obtain linear in time growth for the
vorticity gradient for all times, for certain smooth and compactly supported
initial vorticity in $\mathbb{R}^2$. The construction carries over to some
generalized SQG equations.
