Near-surface flows measured by the ring-diagram technique of local helioseismology show structures that persist over multiple rotations. We examine these phenomena using data from the {em Global Oscillation Network Group} (GONG) and the {em Helioseismic and Magnetic Imager} (HMI) and show that a correlation analysis of the structures can be used to estimate the rotation rate as a function of latitude, giving a result consistent with the near-surface rate from global helioseismology and slightly slower than that obtained from a similar analysis of the surface magnetic field strength. At latitudes of 60$^{circ}$ and above the HMI flow data reveal a strong signature of a two-sided zonal flow structure. This signature may be related to recent reports of giant cells in solar convection.