A realistic numerical model was constructed to simulate the oceanic conditions and circulation in a large southeast Greenland fjord (Kangerdlugssuaq) and the adjacent shelf sea region during winter 2007-2008. The major outlet glaciers in this region recently destabilised, contributing to sea level rise and ocean freshening, with increased oceanic heating a probable trigger. It is not apparent a priori whether the fjord dynamics will be influenced by rotational effects, as the fjord width is comparable to the internal Rossby radius. The modelled currents, however, describe a highly three-dimensional system, where rotational effects are of order-one importance. Along-shelf wind events drive a rapid baroclinic exchange, mediated by coastally trapped waves (CTWs) which propagate from the shelf to the glacier terminus along the right-hand boundary of the fjord. The terminus was regularly exposed to around 0.5 TW of heating over the winter season. Wave energy dissipation provoked vertical mixing, generating a buoyancy flux which strengthened overturning. The CTWs also acted to strengthen the cyclonic mean flow via Stokes' drift. Although the outgoing wave was less energetic and located at the opposite sidewall, the fjord did exhibit a resonant response, suggesting that fjords of this scale can also exhibit two-dimensional dynamics. Long periods of moderate wind stress greatly enhanced the cross-shelf delivery of heat towards the fjord, in comparison to stronger events over short intervals. This suggests that the timescale over which the shelf wind field varies is a key parameter in dictating wintertime heat delivery from the ocean to the ice sheet.