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

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The mass redistribution associated with the Quaternary glacial cycles, with a cycle of approximately 90kiloyears glaciation and 10kiloyears 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 (ηl) influences significantly on the predictions. In a weak frictional coupling case, the differential rotation of both cores amounts to 5×10-10rads-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 ηl~1022Pas. The predictions are sensitive to the frictional torques at the CMB and ICB. If the strength of the poloidal field at the ICB (Bp) is larger than the half at the CMB, then both cores rotate at a similar rate. The critical poloidal strength (Bpc), of course, depends on an uncertain value of the conductivity at the top of the inner core. In the case of Bp

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