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We establish a number of results that reveal a form of irreversibility(distinguishing arbitrarily long from finite time) in 2d Euler flows, by virtueof twisting of the particle trajectory map. Our main observation is thattwisting in Hamiltonian flows on annular domains, which can be quantified bythe differential winding of particles around the center of the annulus, isstable to perturbations. In fact, it is possible to prove the stability of thewhole of the lifted dynamics to non-autonomous perturbations (though singleparticle paths are generically unstable). These all-time stability facts areused to establish a number of results related to the long-time behavior ofinviscid fluid flows. In particular, we show that nearby general stable steadystates (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 tothe SQG equation and of smooth vortex patch solutions to the Euler equationthat entangle and develop unbounded perimeter in infinite time.

Twisting in Hamiltonian Flows and Perfect Fluids