Fluctuations of the Earth's dynamic oblateness J2 are a measure of global redistributions of mass between equatorial and polar regions, sensitive to the component which is symmetric about the equator. Cox and Chao recently published a time series of monthly values of J2 based on satellite orbit determination, which showed rapid fluctuations from month to month, as well as a large change in J2 in 1997/1998. We here investigate the ocean dynamics associated with these rapid fluctuations using a barotropic ocean model forced by atmospheric wind stress and pressure. We find that the model has significant skill in reproducing the observations, though not the change in 1997/1998. Much of the model variability is related to coherent circumpolar fluctuations in Arctic and Antarctic bottom pressure which, despite their apparent symmetry, are forced by quite different mechanisms. The Antarctic mode is forced by circumpolar winds, whereas the Arctic mode is forced by northward winds over the entrances to the polar sea. Comparison with in situ observations shows that the model has skill in reproducing the polar modes. Arctic tide gauge records confirm the presence of a coherent mode at short periods, and at long periods over at least the Eurasian Arctic shelf. If barotropic, and representative of the whole Arctic, this would be large enough to make a major contribution to measured J2 fluctuations, but does not account for the 1997/1998 event.