  We establish a number of results that reveal a form of irreversibility
(distinguishing arbitrarily long from finite time) in 2d Euler flows, by virtue
of twisting of the particle trajectory map. Our main observation is that
twisting in Hamiltonian flows on annular domains, which can be quantified by
the differential winding of particles around the center of the annulus, is
stable to perturbations. In fact, it is possible to prove the stability of the
whole of the lifted dynamics to non-autonomous perturbations (though single
particle paths are generically unstable). These all-time stability facts are
used to establish a number of results related to the long-time behavior of
inviscid fluid flows. In particular, we show that nearby general stable steady
states (i) all Euler flows exhibit indefinite twisting and hence "age", (ii)
vorticity generically becomes filamented and exhibits wandering in $L^\infty$.
We also give examples of infinite time gradient growth for smooth solutions to
the SQG equation and of smooth vortex patch solutions to the Euler equation
that entangle and develop unbounded perimeter in infinite time.
