We study the temporal variation of subsurface flows associated with active regions within 16 Mm of the solar surface. We have analyzed the subsurface flows of nearly 1000 active and quiet regions applying ring-diagram analysis to Global Oscillation Network Group (GONG) Dopplergram data. We find that newly emerging active regions are characterized by enhanced upflows and fast zonal flows in the near-surface layers, as expected for a flux tube rising from deeper layers of the convection zone. The subsurface flows associated with strong active regions are highly twisted, as indicated by their large vorticity and helicity values. The dipolar pattern exhibited by the zonal and meridional vorticity component leads to the interpretation that these subsurface flows resemble vortex rings, when measured on the spatial scales of the standard ring-diagram analysis.