The ocean's baroclinic response to a steadily moving storm is analyzed using a numerical model for an inviscid, multi-layered fluid. This first part of a two-part study gives a detailed account of the response to a rapidly moving hurricane, while parameter dependence is examined in the second part. A central theme of both parts is the coupling between wind-forcing, the surface mixed layer, and the thermocline. The baroclinic response is made up of a geostrophic component and a three-dimensional wake of inertial-internal waves which is emphasized. These waves initially have large horizontal spatial scales set directly by the storm. Their along-storm track wavelength is the storm translation speed times the wave period, which is typically five percent less than the local inertial period. Their cross-track scale is the storm scale. If the storm is intense as it is here, finite amplitude effects soon produce a double inertial frequency wave and smaller spatial scales. An important qualitative result ... Abstract The ocean's baroclinic response to a steadily moving storm is analyzed using a numerical model for an inviscid, multi-layered fluid. This first part of a two-part study gives a detailed account of the response to a rapidly moving hurricane, while parameter dependence is examined in the second part. A central theme of both parts is the coupling between wind-forcing, the surface mixed layer, and the thermocline. The baroclinic response is made up of a geostrophic component and a three-dimensional wake of inertial-internal waves which is emphasized. These waves initially have large horizontal spatial scales set directly by the storm. Their along-storm track wavelength is the storm translation speed times the wave period, which is typically five percent less than the local inertial period. Their cross-track scale is the storm scale. If the storm is intense as it is here, finite amplitude effects soon produce a double inertial frequency wave and smaller spatial scales. An important qualitative result ...