A non-hydrostatic numerical weather prediction model has been employed to simulate idealised katabatic flows over a moderate slope and adjoining ice shelf. To be specific, the topography of Coats Land and the adjoining Brunt Ice Shelf, Antarctica, have been used, although this is typical of much of the Antarctic coastline. The RAMS (Regional Atmospheric Modeling System) Version 4.3 has been adapted for simulations over compacted snow, most notably through changes to the multi-layer soil model. The simulations are initialised using clear-sky climatological conditions and at rest. A shallow katabatic flow develops into a quasi steady-state after about 12 hours of simulation time. The peak downslope winds are ~7 m s-1 at 30 m above the surface near the steepest part of the slope. The flow depth ranges from 50 to 100 m down the slope. Over the ice shelf, the katabatic flow peters out, while a pool of cold air develops, primarily through sensible heat loss into the surface and partially balancing the net radiative heat loss to space. Near-surface and sounding data from the model simulations compare well with archetypal and typical katabatic flow observations; especially after some tuning of the model's turbulence parameterisation. An analysis of the downslope flow dynamics shows the buoyancy force is generally balanced by the inertial force; except towards the foot of the slope, where the buoyancy force is balanced by up-slope thermal wind forces due to the pool of cold air over the ice shelf. Over time, the cooling of the ice shelf boundary layer leads to an apparent retreat of the katabatic flow from the ice shelf and some way up the slope. The analysis explains the observed surface climatology of Coats Land, where the persistent katabatic winds rarely reach the Brunt Ice Shelf. The simulated katabatic flow moves from shooting to tranquil towards the slope foot. This transition acts to trigger a train of internal gravity waves which propagate energy upwards away from the katabatic flow jump. Previous studies have also found shooting to tranquil katabatic flow transitions, so to generalise these findings would suggest that internal gravity wave generation is ubiquitous around much of coastal Antarctica and Greenland.