In this study we look at the ocean circulation of the Arctic Ocean in the high-resolution OCCAM global ocean model. The Arctic Ocean consists of deep basins surrounded by a large area of continental shelves, where cooling and ice formation play an important role in dense water formation. In the model these dense waters are transported by a circumpolar boundary current into the deep convection sites of the North Atlantic Ocean. The boundary current is thought to be a continuous feature in the real ocean, however the driving force is still unknown. We provide evidence that buoyancy fluxes that occur due to air-sea exchanges on the continental shelves are an important driving force for the boundary current in the model. The formation area of the circumpolar boundary current is found in the Barents Sea, where there is a high pressure area associated with cooling of inflowing Atlantic Water (AW). The modified water, Barents Sea Water (BSW), is then able to pass through the Arctic Front as it sinks into the Arctic Basin via the St Anna Trough in a boundary current. The high density signal of these waters can be seen all around the continental slope of the Arctic Ocean as a continuous pressure gradient. The boundary pressure gradient continues into the North Atlantic, where a low pressure region is found off Cape Hatteras. A time-dependent variant of an accurate particle tracking technique has been applied to calculate pathways of the dense waters using stored velocity fields of the OCCAM model. This technique has been extended with a representation of random motions due to diffusive effects. An expression for the random motions is derived using the theory of Brownian motion, and is chosen to match the Laplacian eddy viscosity terms in the momentum equations of the OCCAM model. The trajectories of the dense waters on the Barents Sea shelf follow the boundary current, and are guided around the slope by topographical contours. However the pathways are severely affected by large-scale wind-driven features as the Trans-Arctic drift and the Beaufort Gyre, which carry water masses out of the boundary current or trap them in the Canadian Basin. It is found that it takes approximately 30 years for the bulk of BSW to reach the North Atlantic, although the major signals complete the Arctic circumference within 10 years. The transport of the BSW through the Arctic into the North Atlantic can be accurately described by a 1D advection-diffusion model with a ”diffusion” coefficient of 1.3 · 109cm2/s and an ”advection” coefficient of 2.9cm/s. This confirms that the diffusion of particles is caused by basin-scale features rather than meso-scale eddies. More dense water is formed on the Chukchi Sea shelf, which originates from the Bering Strait Outflow. There are signs that these dense waters provide forcing for eddies seen off North Alaska. A new theory is presented for calculating the Available Potential Energy (APE) on the continental shelves for driving local currents in the Arctic Ocean, using the mean offshore density structure as a reference state. The air-sea fluxes in the Barents Sea are found to create a large amount of APE on the shelves, which is lost as the dense waters sink into the Arctic Basin. Although it is found the inflowing AW already has a large amount of APE which cannot fully be converted due to the Arctic Front in Fram Strait, therefore it appears the cooling in the Barents Sea is crucial to the forcing of the boundary current. This cooling in the prescribed model air-sea fluxes is likely to be caused by enormous heat losses to the atmosphere in large ice-free regions, which are created by the inflow of warm AW.