  Motivated by the pop-stack-sorting map on the symmetric groups, Defant
defined an operator $\mathsf{Pop}_M : M \to M$ for each complete
meet-semilattice $M$ by $$\mathsf{Pop}_M(x)=\bigwedge(\{y\in M: y\lessdot
x\}\cup \{x\}).$$ This paper concerns the dynamics of
$\mathsf{Pop}_{\mathrm{Tam}_n}$, where $\mathrm{Tam}_n$ is the $n$-th Tamari
lattice.
  We say an element $x\in \mathrm{Tam}_n$ is $t$-$\mathsf{Pop}$-sortable if
$\mathsf{Pop}_M^t (x)$ is the minimal element and we let $h_t(n)$ denote the
number of $t$-$\mathsf{Pop}$-sortable elements in $\mathrm{Tam}_n$. We find an
explicit formula for the generating function $\sum_{n\ge 1}h_t(n)z^n$ and
verify Defant's conjecture that it is rational. We furthermore prove that the
size of the image of $\mathsf{Pop}_{\mathrm{Tam}_n}$ is the Motzkin number
$M_n$, settling a conjecture of Defant and Williams.
