  We show that interferometry can be applied to study irregular, rapidly
rotating structures, as are expected in the turbulent accretion flow near a
black hole. Specifically, we analyze the lagged covariance between
interferometric baselines of similar lengths but slightly different
orientations. For a flow viewed close to face-on, we demonstrate that the peak
in the lagged covariance indicates the direction and angular velocity of the
emission pattern from the flow. Even for moderately inclined flows, the
covariance robustly estimates the flow direction, although the estimated
angular velocity can be significantly biased. Importantly, measuring the
direction of the flow as clockwise or counterclockwise on the sky breaks a
degeneracy in accretion disk inclinations when analyzing time-averaged images
alone. We explore the potential efficacy of our technique using
three-dimensional, general relativistic magnetohydrodynamic (GRMHD)
simulations, and we highlight several baseline pairs for the Event Horizon
Telescope (EHT) that are well-suited to this application. These results
indicate that the EHT may be capable of estimating the direction and angular
velocity of the emitting material near Sagittarius A*, and they suggest that a
rotating flow may even be utilized to improve imaging capabilities.
