The 'geodynamo' in the Earth's liquid outer core produces a magnetic field that dominates the large and medium length scales of the magnetic field observed at the Earth's surface. Here we use data from the currently operating Danish Oersted satellite, and from the US Magsat satellite that operated in 1979/80, to identify and interpret variations in the magnetic field over the past 20 years, down to length scales previously inaccessible. Projected down to the surface of the Earth's core, we found these variations to be small below the Pacific Ocean, and large at polar latitudes and in a region centred below southern Africa. The flow pattern at the surface of the core that we calculate to account for these changes is characterized by a westward flow concentrated in retrograde polar vortices and an asymmetric ring where prograde vortices are correlated with highs (and retrograde vortices with lows) in the historical (400-year average) magnetic field. This pattern is analogous to those seen in a large class of numerical dynamo simulations, except for its longitudinal asymmetry. If this asymmetric state was reached often in the past, it might account for several persistent patterns observed in the palaeomagnetic field. We postulate that it might also be a state in which the geodynamo operates before reversing.