HR: 11:40h
AN: T31G-05    [PDF]
TI: The power requirement of the geodynamo from scaling Joule dissipation in numerical models
AU: * Christensen, U R
EM: christensen@linmpi.mpg.de
AF: Max-Planck Institute for Aeronomy, Max-Planck Strasse 2, Katlenburg-Lindau, 37191 Germany
AB: In order to contrain models of the thermal evolution of the core, the nucleation time of the inner core and possible requirements for core heat sources, the power needed to maintain the geomagnetic field against Joule dissipation must be known. Here I use results from a large number of convection-driven spherical shell MHD dynamo models to derive a systematic scaling of the magnetic decay time $\tau$, defined as the time-average of magnetic energy over Joule dissipation. The magnetic Reynolds number $Rm$ covers the range between $50$ and $1000$, Ekman numbers are between $3\times10^{-4}$ and $10^{-5}$, and magnetic Prandtl numbers $Pm$ between $0.25$ and $3$. The results are fitted fairly well by a simple relation of the form $\tau \sim Rm^{-1}$. A weak dependence on the magnetic Prandtl number may exist and a two-parameter fit of the form $\tau \sim Rm^{-1} Pm^{1/6}$ reduces the scatter somewhat. I use a ratio of $\approx 7$ between the mean field strength inside the fluid shell and at its surface, taken from a model with a particularly Earth-like field, to estimate the magnetic energy density in the core as $3 J/m^3$. For $Rm=500$ the simple scaling of magnetic decay time predicts a Joule dissipation of $3\times10^{11} W$ in the core. When a dependence on the magnetic Prandtl number is assumed, this figure rises to $3\times10^{12} W$. While the former value can be easily accommodated in the energy budget of the core, the second one puts severe constraints on its thermal history and energetics.
DE: 1015 Composition of the core
DE: 1507 Core processes (8115)
DE: 1510 Dynamo theories
SC: Tectonophysics [T]
MN: 2003 Fall Meeting