Convection in the Arctic Ocean mixed layer occurs under openings in sea ice where new sea ice is formed. The process of brine rejection during ice formation creates negatively buoyant fluid at the surface of ice leads. When the fluid convects downward the ocean mixed layer below the lead is stirred vertically and, through planetary rotational effects, along-lead flows at the lead edges are induced. These vertical and lateral motions have been previously studied using two-dimensional numerical ocean models and observed in field programs such as LeadEx. In this paper the generation of Arctic Ocean eddies through dynamic instabilities is investigated using a three-dimensional, nonhydrostatic ocean model. Results suggest that salt-enriched vortices can develop at the base of the mixed layer as a consequence of brine rejection, but the vortex formation requires a time period of several days, a time long enough that the progenitor lead would likely have closed. The scale of the eddies is found to depend on the magnitude of the buoyancy forcing, the width of the lead, and the duration of the buoyancy forcing. The number of vortices produced depends on lead width and duration of buoyancy forcing but is less sensitive to the magnitude of the buoyancy forcing. Vortex sizes, scaled appropriately, and vortex numbers are compared with those found in recent laboratory studies of convectively driven flows from line segment sources.