Mean-field view on geodynamo models [Elektronische Ressource] / vorgelegt von Martin Schrinner

Mean-field view on geodynamo modelsDissertationzur Erlangung des Doktorgradesder Mathematisch-Naturwissenschaftlichen Fakultaten¨der Georg-August-Universitat¨ zu Gottingen¨vorgelegt vonMartin Schrinneraus EschwegeGottingen¨ 2005D7Referent: Prof. Dr. A. TilgnerKorreferent: Prof. Dr. U. ChristensenTag der mundlichen¨ Prufung:¨ 13.7.2005ContentsSummary 51 Introduction 72 Numerical modelling of the geodynamo 132.1 Model equations............................... 132.2 Numerical techniques ............................ 143 Mean-field theory 173.1 The mean-field concept ........................... 173.2 Mean-field coefficients in spherical geometry ............... 193.3 The second order correlation approximation ................ 23.4 Symmetry properties of mean-field coefficients .............. 234 How to derive mean-field coefficients 274.1 Approach (I)................................. 274.1.1 The method ............................. 274.1.2 The choice of test fields ...................... 294.2 Approach (II) ................................ 305 Mean-field coefficients: results 355.1 Simulation of rotating magnetoconvection ................. 355.1.1 Velocity and magnetic field..................... 355.1.2 Non-covariant and covariant mean-field coefficients........ 375.1.3 Isotropic approximation ...................... 425.1.4 α- and β-quenching ........................ 425.2 A simple quasi-stationary dynamo 475.2.