16. Numerical Dynamo Simulations: From Basic Concepts to Realistic Models

The last years have witnessed an impressive growth in the number and quality of numerical dynamo simulations. The numerical models successfully describe many aspects of the geomagnetic field and also set out to explain the various fields of other planets. The success is somewhat surprising since numerical limitation force dynamo modelers to run their models at unrealistic parameters. In particular the Ekman number, a measure for the relative importance of viscous to Coriolis forces, is many orders of magnitude too large: Earth’s Ekman number is E = 10 ^{− 15} while even today’s most advanced numerical simulations have to content themselves with E = 10 ^{− 6}. After giving a brief introduction into the basics of modern dynamo simulations the fundamental force balances are discussed and the question how well the modern models reproduce the geomagnetic field is addressed. First-level properties like the dipole dominance, realistic Elsasser and magnetic Reynolds numbers, and an Earth-like reversal behavior are already captured by larger Ekman number simulations around E = 10 ^{− 3}. However, low Ekman numbers are required for modeling torsional oscillations which are thought to be an important part of the decadal geomagnetic field variations. Moreover, only low Ekman number models seem to retain the huge dipole dominance of the geomagnetic field once the Rayleigh number has been increased to values where field reversals happen. These cases also seem to resemble the low-latitude field found at Earth’s core-mantle boundary more closely than larger Ekman numbers cases.