An analytical model describing the evolution of a convective atmospheric boundary layer in marine cold-air outbreaks in the Arctic is presented. The novelty of the model is a detailed description of the baroclinicity associated with the boundary-layer growth and heating. Ekman friction is also taken into account. Thereby, the model describes the evolution of mixed- layer wind components over the ocean. It is shown theoretically that baroclinicity leads either to deceleration or to acceleration of the flow over the ocean, which depends on the direction of the large-scale flow relative to the orientation of the ice edge. Acceleration of the flow leads to a formation of a low-level jet strongly affecting the surface fluxes of heat and momentum. Baroclinicity and the magnitude of the low-level jet are strongest close to the ice edge being proportional to the ocean-ice temperature difference and decays further downwind. Horizontal decay of the low-level jet strength is governed by the airmass transformation length scale which is estimated to be in the order of 500-1000 km for typical cold-air outbreaks. The model solutions are shown to be in good agreement with aircraft observations over the Fram Strait and results of a numerical nonhydrostatic model.