Core–mantle coupling including a viscoelastic inner core: an application to the axial rotation associated with the Quaternary glacial cycles

Abstract

The mass redistribution associated with the Quaternary glacial cycles, with a cycle of approximately 90 kiloyears glaciation and 10 kiloyears deglaciation phases, causes differential rotations of the outer and inner cores relative to the mantle. The differential rotations are examined for an earth model composed of incompressible Maxwell viscoelastic mantle, inviscid outer core and incompressible Maxwell viscoelastic inner core. A quasi-rigid rotation is assumed for both cores, and viscous and electromagnetic torques at the core–mantle boundaries (CMB) and inner core boundaries (ICB) are taken into account. The effect of the inner core viscosity is negligibly small, but the lower mantle viscosity ( η l) influences significantly on the predictions. In a weak frictional coupling case, the differential rotation of both cores amounts to 5×10 −10 rad s −1 (∼0.9° per year) at the end of the deglaciation. Its magnitude gradually increases with increasing lower mantle viscosity, and generally approaches to a constant value at η l∼10 22 Pa s. The predictions are sensitive to the frictional torques at the CMB and ICB. If the strength of the poloidal field at the ICB ( B p) is larger than the half at the CMB, then both cores rotate at a similar rate. The critical poloidal strength ( B pc), of course, depends on an uncertain value of the conductivity at the top of the inner core. In the case of B p< B pc, significant differential rotation between the outer and inner cores (<3×10 −10 rad s −1) is predicted for a plausible range of the torque at the CMB. Moreover, the predictions at the present-day indicate a westward drift for the outer core and eastward drift for the inner core in some cases with B p< B pc and 3×10 21 Pa s ≤η l ≤6×10 21 Pa s. The magnitude of the outer and inner cores is, however, less than 5×10 −11 and 1×10 −10 rad s −1, respectively. The response to rapid potential variations, corresponding to a pulse-like sea-level change such as meltwater pulse observed at 14 kiloyears BP, is dominantly elastic, and takes a maximum value of ∼10 −10 rad s −1 (∼0.2° per year). The acceleration for this response, however, reaches ∼10 −20 rad s −2, significantly larger than the maximum estimate of ∼10 −21 rad s −2 for an average potential variation model. Time series of the predicted differential rotation may be grouped into three distinctive types from the degree of the coupling at the CMB. In a relatively weak coupling case, the predictions are approximately similar to an average sea-level change of the Quaternary glacial cycles and the spectrum evaluated from the time series has a sharp peak at the period of about 100 kiloyears. In a strong coupling case, the dominant signals are due to the pulse-like potential variations, resulting in a white spectrum.