  In laboratory studies and numerical simulations, we observe clear signatures
of unstable time-periodic solutions in a moderately turbulent
quasi-two-dimensional flow. We validate the dynamical relevance of such
solutions by demonstrating that turbulent flows in both experiment and numerics
transiently display time-periodic dynamics when they shadow unstable periodic
orbits (UPOs). We show that UPOs we computed are also statistically
significant, with turbulent flows spending a sizable fraction of the total time
near these solutions. As a result, the average rates of energy input and
dissipation for the turbulent flow and frequently visited UPOs differ only by a
few percent.
