The connections between Greenland’s tidewater glaciers and the continental shelf waters are modulated by fjords that are geometrically complex with numerous modes of variability. These fjords transport heat towards the glaciers and meltwater away, with a renewal determined by a range of factors including buoyancy forcing at the surface (surface melt) and at depth (subglacial discharge), wind stresses, shelf currents, bathymetry, and mixing processes. This study aims to classify the various regimes of flow and fjord renewal over the diverse parameter space of Greenland fjords with an emphasis on investigating the role of shelf-driven variability and mixing. We conduct idealized numerical simulations using MITgcm to explore how fjord renewal is controlled by elements of the shelf and fjord geometry, and by thermodynamic and mechanical forcings, with domains consisting of idealized bays and shelves representative of Greenland. Specifically, we investigate the sensitivity of the renewal to the following dynamic/thermodynamic influences: (a) bathymetric sills and their influence on mixing, (b) horizontal constrictions (peninsulas, islands, turns), (c) ice cover, and (d) subglacial meltwater discharge. To explain our numerical model results, we develop dynamical theories for the exchange flow as a function of the geometric and forcing parameters.