The transport of low-salinity waters through the Canadian Arctic Archipelago links the North Pacific, Arctic, and North Atlantic Oceans. This transport is influenced by many related small-scale processes including mixing, internal hydraulics, and internal tide generation. In this thesis, I quantify and elucidate the physics of such processes with aims of addressing discrepancies between observed and simulated fluxes through the Archipelago and advancing the skill of numerical models by identifying shortcomings and informing where and how progress can be achieved. To address the dearth of mixing rates across the network of channels, I first use a large-scale model to obtain baseline estimates of the spatial and seasonal variability of the vertical buoyancy flux. Much of the mixing occurs in the eastern half of the Archipelago and is attributed to the abundance of sills and narrow channels. Indeed, the so-called 'central sills area' is shown to be a mixing hot spot. I investigate this region further using high-spatial-resolution observational transects to examine the role of tides, which are excluded from the large-scale model. The many shallow channels here accelerate tidal currents and thereby induce strong bottom boundary layer dissipation. This is the largest energy sink within an observationally constrained energy budget. The generation of internal tides is another primary sink of barotropic tidal energy. Because the study site lies poleward of the critical latitudes of the dominant tidal constituents, internal tides propagate as internal Kelvin waves. Idealized, process-oriented modelling demonstrates that the amplitudes of such waves, or similarly the energy extracted from the barotropic tide, is sensitive to channel width because waves generated at each side of the channel interfere. Given the multiple connecting channels of the Archipelago, it is difficult to make a priori estimates of internal tide generation for a given channel. Nevertheless, the phenomenology I describe will be detectable in, and a requisite to understanding, pan-Arctic or global three-dimensional tidal models, which are becoming more prevalent. / Graduate