The geodynamo requires that at least part of the Earth's liquid core be convecting so vigorously as to mix it thoroughly to uniform composition and adiabatic temperature. It is possible, however, that part of liquid core is stably stratified, either thermally because of a low temperature gradient or compositionally because light material has separated out. The top of the outer core is the most likely site for stability because the adiabat is steepest there and because light material will rise to the surface. Here I show that part of the observed secular variation, that associated with flux expulsion in the southern hemisphere, can only be caused by fluid upwelling in the electromagnetic boundary layer at the top of the core or by very strong poloidal field gradients at the top of the core. Any stratified layer is limited to roughly the uppermost 100 km if flux expulsion is the mechanism; if the layer is any thicker the region in the southern hemisphere where reverse flux patches are growing must also be the site of very strong field gradients caused by very strong near-surface shear flows.
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