Timescales of geomagnetic secular acceleration in satellite field models and geodynamo models

Magnetic satellite data from the last decade allow to model geomagnetic secular acceleration, the second time derivative of the field, in a highly precise manner. Robust estimates of the secular acceleration (SA) are obtained by using order six B-Splines as representation of the field variability, which in turn allows us to estimate the characteristic SA timescale, tSA. We confirm a recent finding that tSA is of order 10 years and fairly independent of the spherical harmonic degree n. This contrasts with the characteristic timescale of geomagnetic secular variation tSV, which is a decreasing function of n and is 100 yr for n= 5. Conceivably the SA timescale might be related to short-term processes in the core, distinct from convective overturn whose timescale is reflected by tSV. Previously it had been shown that dynamo simulations reproduce the shape of the secular variation (SV) spectrum and, provided their magnetic Reynolds number Rm has an Earth-like value of order 1000, also the absolute values of tSV. The question arises if dynamo simulations can capture the observed timescales of geomagnetic SA. We determined tSA(n) for a set of dynamo models, covering a range of values of the relevant control parameters. The selection of models was based on the morphological similarity of their magnetic fields to the geomagnetic field and not on criteria related to the time dependence of the field, or on any aspect of the spectra associated with their field variation. We find that tSA depends only weakly on n up to degree 10, but for larger n it asymptotically approaches the 1/n-dependence that is also found for tSV(n). The acceleration timescale at low n varies with magnetic Reynolds number more strongly than tSV and may also depend on magnetic field strength. For an Earth-like Rm 1000, tSA is of order 10 yr for n? 210, as found in the field models from satellite data. A simple scaling analysis based on the frozen flux assumption for magnetic variations suggests two contributions to the SA, an advective part that scales with velocity U and has a length scale dependence corresponding to n-1, and a part that depends on the acceleration of the flow without explicit dependence on the length scale. Their combination can explain the spectral shape of tSA(n) in numerical models, with the latter term dominating at n < 10. The characteristic timescale of acceleration of the near surface flow correlates with tSA in the different numerical models and is of the same order as tSA. This suggests that the observed 10 yr timescale of geomagnetic SA reflects the characteristic time of core flow acceleration. To explain the geomagnetic SV and SA timescales, we find that the rms velocity near the core surface must be 18 km yr-1 and the rms flow acceleration approximately 2 km yr-2, although a statistical analysis of the induction equation suggests that most of the latter may occur at flow scales corresponding to harmonic degrees n > 12. The ability of dynamo models to match simultaneously SV and SA timescales suggests that dynamic processes in the core at the decadal timescale are not fundamentally different from those at the centennial timescale.