In the Earth's fluid outer core, a dynamo process converts thermal and gravitational energy into magnetic energy. The power needed to sustain the geomagnetic field is set by the ohmic losses (dissipation due to electrical resistance). Recent estimates of ohmic losses cover a wide range, from 0.1 to 3.5 TW, or roughly 0.3-10% of the Earth's surface heat flow. The energy requirement of the dynamo puts constraints on the thermal budget and evolution of the core through Earth's history. Here we use a set of numerical dynamo models to derive scaling relations between the core's characteristic dissipation time and the core's magnetic and hydrodynamic Reynolds numbers--dimensionless numbers that measure the ratio of advective transport to magnetic and viscous diffusion, respectively. The ohmic dissipation of the Karlsruhe dynamo experiment supports a simple dependence on the magnetic Reynolds number alone, indicating that flow turbulence in the experiment and in the Earth's core has little influence on its characteristic dissipation time. We use these results to predict moderate ohmic dissipation in the range of 0.2-0.5 TW, which removes the need for strong radioactive heating in the core and allows the age of the solid inner core to exceed 2.5 billion years.

No abstract

Direct numerical simulations of Rayleigh-Bénard convection in a plane layer with periodic boundary conditions at Rayleigh numbers up to 10(7) show that flow structures can be objectively classified as large or small scale structures because of a gap in spatial spectra. The typical size of the large scale structures does not always vary monotonically as a function of the Rayleigh number but broadly increases with increasing Rayleigh number. A mean flow (whose average over horizontal planes differs from zero) is also excited but is weak in comparison with the large scale structures. The large scale circulation observed in experiments should therefore be a manifestation of the large scale structures identified here.

The dynamo effect is demonstrated numerically in precession driven flow in a spherical container. Both laminar as well as unstable flows act as dynamos. At low Ekman numbers in unstable flows, the dynamo mechanism relies predominantly on the components of the flow excited by instabilities. All calculations are performed in a frame of reference attached to the boundaries. In this frame, the rotation axis of the fluid executes a periodic motion with a period equal to the rotation period of the boundaries, whereas the magnetic dipole moment undergoes slower variations interrupted by reversals.

No abstract