The ocean circulation is forced at a global scale by winds and fluxes of heat and fresh water. Kinetic energy is dissipated at much smaller scales in the turbulent boundary layers and in the ocean interior1,2, where turbulent mixing controls the transport and storage of tracers such as heat and carbon dioxide3,4. The primary site of wind power input is the Southern Ocean, where the westerly winds are aligned with the Antarctic Circumpolar Current5. The potential energy created here is converted into a vigorous geostrophic eddy field through baroclinic instabilities. The eddy energy can power mixing in the ocean interior6–8, but the mechanisms governing energy transfer to the dissipation scale are poorly constrained. Here we present simulations that simultaneously resolve meso- and submeso-scale motions as well as internalwaves generated by topography in the Southern Ocean. In our simulations, more than 80% of the wind power input is converted from geostrophic eddies to smaller-scale motions in the abyssal ocean. The conversion is catalysed by rough, small-scale topography. The bulk of the energy is dissipated within the bottom 100m of the ocean, but about 20% is radiated and dissipated away from topography in the ocean interior, where it can sustain turbulent mixing. We conclude that in the absence of rough topography, the turbulent mixing in the ocean interiorwould be diminished.