Changes in the rate of ocean‐driven basal melting of Antarctica's ice shelves can alter the rate at which the grounded ice sheet loses mass and contributes to sea level change. Melt rates depend on the inflow of ocean heat, which occurs through steady circulation and eddy fluxes. Previous studies have demonstrated the importance of eddy fluxes for ice shelves affected by relatively warm intrusions of Circumpolar Deep Water. However, ice shelves on cold water continental shelves primarily melt from dense shelf water near the grounding line and from light surface water at the ice shelf front. Eddy effects on basal melt of these ice shelves have not been studied. We investigate where and when a regional ocean model of the Ross Sea resolves eddies and determine the effect of eddy processes on basal melt. The size of the eddies formed depends on water column stratification and latitude. We use simulations at horizontal grid resolutions of 5 and 1.5 km and, in the 1.5‐km model, vary the degree of topography smoothing. The higher‐resolution models generate about 2–2.5 times as many eddies as the low‐resolution model. In all simulations, eddies cross the ice shelf front in both directions. However, there is no significant change in basal melt between low‐ and high‐resolution simulations. We conclude that higher‐resolution models (<1 km) are required to better represent eddies in the Ross Sea but hypothesize that basal melt of the Ross Ice Shelf is relatively insensitive to our ability to fully resolve the eddy field.