  The black-hole images obtained with the Event Horizon Telescope (EHT) are
expected to be variable at the dynamical timescale near their horizons. For the
black hole at the center of the M87 galaxy, this timescale (5-61 days) is
comparable to the 6-day extent of the 2017 EHT observations. Closure phases
along baseline triangles are robust interferometric observables that are
sensitive to the expected structural changes of the images but are free of
station-based atmospheric and instrumental errors. We explored the day-to-day
variability in closure phase measurements on all six linearly independent
non-trivial baseline triangles that can be formed from the 2017 observations.
We showed that three triangles exhibit very low day-to-day variability, with a
dispersion of $\sim3-5^\circ$. The only triangles that exhibit substantially
higher variability ($\sim90-180^\circ$) are the ones with baselines that cross
visibility amplitude minima on the $u-v$ plane, as expected from theoretical
modeling. We used two sets of General Relativistic magnetohydrodynamic
simulations to explore the dependence of the predicted variability on various
black-hole and accretion-flow parameters. We found that changing the magnetic
field configuration, electron temperature model, or black-hole spin has a
marginal effect on the model consistency with the observed level of
variability. On the other hand, the most discriminating image characteristic of
models is the fractional width of the bright ring of emission. Models that best
reproduce the observed small level of variability are characterized by thin
ring-like images with structures dominated by gravitational lensing effects and
thus least affected by turbulence in the accreting plasmas.
