Core‐mantle boundary shape: constraints inferred from the pressure torque acting between the core and the mantle

SUMMARY In the last few years, models of the flow at the top of the Earth's core and of the related pressure field have been calculated from the secular variation of the geomagnetic field, and core‐mantle topographies have been computed by seismologists. A pressure torque results from the action of the pressure field on the core topography which can theoretically be computed from models of both the pressure field and the core‐mantle interface. Small‐scale features of the flow and of the topography are shown to be capable of contributing strongly to the pressure torque; it is thus impossible to calculate the exact value of the torque from the knowledge of only the long‐wavelength components of the models. But the interaction between the large‐scale components generates by itself torques two orders of magnitude larger than the torques inferred from the irregularities of the length of the day. It is nevertheless possible to reconcile the topographic coupling mechanism with the length of the day observations, keeping the amplitude of the core topography proposed by seismologists, if an orthogonality relation between the geometry of the fluid upwellings and downwellings at the top of the core and the topography is satisfied. It is shown how to compute such a topography, for a given flow, and close to an original topography provided by seismic tomography. Some consequences of the so‐inferred link between the fluid flow at the top of the core and the core‐mantle boundary topography are discussed.