AbstractWe are interested here in describing the linear response of a highly rotating fluid to some surface stress tensor, which admits fast time oscillations and may be resonant with the Coriolis force. In addition to the usual Ekman layer, we exhibit another – much larger – boundary layer, and we prove that for large times, the effect of the surface stress may no longer be localized in the vicinity of the surface. From a mathematical point of view, the main novelty here is to introduce some systematic approach for the study of boundary effects.