to be well-described by the Vlasov equations. See e.g. [@BouchetMorita10; @SchecterEtAl00; @Briggs70; @BM95; @MouhotVillani11; @BMT13; @BM13] and the references therein for some discussion about the connections between inviscid damping and Landau damping and the more general concept of phase mixing.

Orr himself pointed out the main subtlety inherent with inviscid damping and Landau damping: in , vorticity can just as easily unmix to large scales and create growth in the velocity field as it can mix to small scales and create decay; together the two effects are known as the *Orr mechanism*. Indeed, if one takes initial data concentrated near frequencies $\eta,k > 0$ with $\eta$ large relative to $k$, one can observe from that the stream-function reaches a maximum amplitude near the *critical time* $t \sim \eta/k$. Even on the linear level, this implies that one needs to *pay regularity* to deduce decay of the velocity, in order to control the amount of information that is being unmixed. See [@Boyd83; @Lindzen88; @BM13] for more discussion of the Orr mechanism. For similar reasons, the enhanced dissipation slows down near the critical times as the enstrophy passes through the $O(1)$ length scales. Hence, it is a serious over-simplification to imagine the 