In this work, models for the Earth's magnetic field and global ocean circulation are combined to produce the first quantitative estimates of the electromagnetic Lorentz forces which couple abyssal ocean layers with the energetic surface layers. Under present conditions these coupling forces are very weak: typical time scales for the transfer of momentum to the lower layers are about three thousand years. But they are worth describing quantitatively because of the following: 1) The coupling rapidly increases in proportion with the square of the Earth's magnetic field strength; 2) This process is intrinsically efficient at accelerating slow or stagnant abyssal ocean layers; 3) These time scales, while long, are similar to those of rapid climate variability which are expected to be associated with past variability in ocean circulation, overturning and heat transport.