The oceanic internal gravity wave spectrum is of interest for several reasons, including the fact that breaking internal waves drive much of the oceanic mixing beneath the mixed layer.  We examine the internal wave spectrum in two recent high-resolution global ocean models -- the HYbrid Coordinate Ocean Model (HYCOM) and the MIT general circulation model (MITgcm) -- that are forced by atmospheric as well as tidal fields.  The spectrum fills out along predicted linear dispersion relation curves, and lies closer to observations when the model resolution is increased.  We discuss implications for satellite altimetry, which can detect the sea surface height signature of the internal gravity wave spectrum, as well as for operational oceanography.