  In this work we are interested in extreme vortex states leading to the
maximum possible growth of palinstrophy in 2D viscous incompressible flows on
periodic domains. This study is a part of a broader research effort motivated
by the question about the finite-time singularity formation in the 3D
Navier-Stokes system and aims at a systematic identification of the most
singular flow behaviors. We extend the results reported in Ayala & Protas
(2013) where extreme vortex states were found leading to the growth of
palinstrophy, both instantaneously and in finite-time, which saturates the
estimates obtained with rigorous methods of mathematical analysis. Here we
uncover the vortex dynamics mechanisms responsible for such extreme behavior in
time-dependent 2D flows. While the maximum palinstrophy growth is achieved at
short times, the corresponding long-time evolution is characterized by some
nontrivial features, such as vortex scattering events.
