Mantle Convection in the Earth and Planets is a comprehensive synthesis of all aspects of mantle convection within the Earth, the terrestrial planets, the Moon, and the Galilean satellites of Jupiter. The book includes up-to-date discussions of the latest research developments that have revolutionized our understanding of the Earth and the planets. It is suitable as a text for graduate courses in geophysics and planetary physics, and as a supplementary reference for use at the undergraduate level. It is also an invaluable review for researchers in the broad fields of the Earth and planetary sciences including seismologists, tectonophysicists, geodesists, mineral physicists, volcanologists, geochemists, geologists, mineralogists, petrologists, paleomagnetists, planetary geologists, and meteoriticists. The book features a comprehensive index, an extensive reference list, numerous illustrations (many in color) and major questions that focus the discussion and suggest avenues of future research.

Numerical calculations of fluid dynamos powered by thermal convection in a rotating, electrically conducting spherical shell are analyzed. We find two regimes of nonreversing, strong field dynamos at Ekman number 10 -4 and Rayleigh numbers up to 11 times critical. In the strongly columnar regime, convection occurs only in the fluid exterior to the inner core tangent cylinder, in the form of narrow columnar vortices elongated parallel to the spin axis. Columnar convection contains large amounts of negative helicity in the northern hemisphere and positive helicity in the southern hemisphere and results in dynamo action above a certain Rayleigh number, through a macroscopic a 2 mechanism. These dynamos equilibrate by generating concentrated magnetic flux bundles that limit the kinetic energy of the convection columns. The dipole-dominated external field is formed by superposition of several flux bundles at middle and high latitudes. At low latitudes a pattern of reversed flux patches propagates in the retrograde direction, resulting in an apparent westward drift of the field in the equatorial region. At higher Rayleigh number we find a fully developed regime with convection inside the tangent cylinder consisting of polar upwelling and azimuthal thermal wind flows. These motions modify the dynamo by expelling poloidal flux from the poles and generating intense toroidal fields in the polar regions near the inner core. Convective dynamos in the fully developed regime exhibit characteristics that can be compared with the geomagnetic field, including concentrated flux bundles on the core-mantle boundary, polar minima in field intensity, and episodes of westward drift. Christensen et al., 1998.] Perhaps the most fimdamental result from these models is the demonstration that rotating convection in a conducting spherical shell produces an external magnetic field dominated by the axial dipole component. The intensity of the axial dipole field in the Glatzmaier-Roberts and Kuang-Bloxham models in particular is comparable to the geomagnetic dipole. The success of numerical dynamo models in reproducing the gross features of the geomagnetic field is encouraging. It suggests that the fluid mechanical processes responsible for generation of the magnetic field in Earth are governed mostly by the fundamental elements in the models, namely convection, rotation, the spherical shell geometry and simple boundary conditions. The broad-scale field structure of convection-driven dynamos appears to be less sensi-10,383 10,384 OLSON ET AL.: NUMERICAL DYNAMO MODELS rive to other model parameters, for example, the way subgrid-scale processes such as turbulence and mixing are parameterized.In this paper we analyze the results of numerical calculations of rotating magnetoconvection leading to dynamos that are dynamically similar to the dynamos referred to above, except that we restrict attention to more modest values of some key dimensionless parameters, specifically the Ekman and Rayleigh numbers, and we treat the inner core in a more simplifie...

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S U M M A RYWe analyse *50 3-D numerical calculations of hydrodynamic dynamos driven by convection in a spherical shell. We examine rigid and stress-free boundaries, with Prandtl number 1, magnetic Prandtl numbers in the range 0.5^5, Ekman numbers E~10 {3^1 0 {4 and Rayleigh numbers to 15 times critical. No parametrizations such as hyperviscosities are used. Successful dynamos are compared with non-magnetic convection solutions. Results for various spectral truncations suggest that the calculations are well resolved when the kinetic and magnetic energy drops by more than two orders of magnitude from the spectral peak to the cut-o¡, although the basic features are still captured at lower resolution. With few exceptions we obtain dipole-dominated magnetic ¢elds. The dynamos operate in the strong-¢eld regime where Lorentz and Coriolis forces are of similar order. The critical magnetic Reynolds number for selfsustained dynamos is of order Rm~50. However, we also ¢nd that the ¢eld can die away when Rm is too large. The minimum magnetic Prandtl number at which we ¢nd dynamo action depends on the Ekman number to the 3/4 power. Dynamos at E~10{3 are subcritical whereas those at E~10 {4 are generally supercritical. The presence of the magnetic ¢eld tends to break the equatorial symmetry of the £ow and favours convection inside the inner core tangent cylinder. With stress-free boundaries, dynamo action suppresses the axisymmetric azimuthal wind that dominates in non-magnetic convection. The ¢eld morphology is broadly similar for both kinds of boundary conditions. When low-pass ¢ltered, several models exhibit ¢eld structures that resemble the geomagnetic ¢eld at the core^mantle boundary to a surprising degree.

Seismic waves sampling the top 100 km of the Earth's inner core reveal that the eastern hemisphere (40 degrees E-180 degrees E) is seismically faster, more isotropic and more attenuating than the western hemisphere. The origin of this hemispherical dichotomy is a challenging problem for our understanding of the Earth as a system of dynamically coupled layers. Previously, laboratory experiments have established that thermal control from the lower mantle can drastically affect fluid flow in the outer core, which in turn can induce textural heterogeneity on the inner core solidification front. The resulting texture should be consistent with other expected manifestations of thermal mantle control on the geodynamo, specifically magnetic flux concentrations in the time-average palaeomagnetic field over the past 5 Myr, and preferred eddy locations in flows imaged below the core-mantle boundary by the analysis of historical geomagnetic secular variation. Here we show that a single model of thermochemical convection and dynamo action can account for all these effects by producing a large-scale, long-term outer core flow that couples the heterogeneity of the inner core with that of the lower mantle. The main feature of this thermochemical 'wind' is a cyclonic circulation below Asia, which concentrates magnetic field on the core-mantle boundary at the observed location and locally agrees with core flow images. This wind also causes anomalously high rates of light element release in the eastern hemisphere of the inner core boundary, suggesting that lateral seismic anomalies at the top of the inner core result from mantle-induced variations in its freezing rate.

Results of fluid dynamical experiments on the behavior of subducted slabs are presented that address two important characteristics of subduction: slab penetration through the transition zone and horizontal slab migration. Cold, negatively buoyant molded slabs of concentrated sucrose solution, with viscosities of 3–5 × 106 P were introduced into a more dilute, two‐layered sucrose solution representing the upper and lower mantle. The transition zone was modeled by a step increase in both density and viscosity. Ratios of slab thickness to upper layer depth, the relative viscosities in each layer, and the effective Rayleigh number were close to mantle values. The initial configuration consisted of two plates separated by a trench gap, with one plate attached to a dipping slab, simulating a developing subduction zone with an overriding plate. Two different boundary conditions were used at the trailing (ridge) end of the subducting plate: (1) fixed end, corresponding to zero ridge motion, and (2) free end, corresponding to zero ridge resistance. Based on results from 15 experiments with various combinations of upper layer, lower layer, and slab densities (ρU, ρL, ρS) and viscosities, we find that slab penetration depth is sensitive to both the normalized slab density anomaly R = (ρS ‐ ρL)/(ρS ‐ ρU) and the dip angle. Three penetration regimes are recognized: R ≳ 0.5, in which the slab sinks into the lower layer without distortion; −0.2 ≲ R ≲ 0.5, which permits limited penetration, the amount dependent on dip angle (in this regime the slab develops a thick root just beneath the transition zone); and R < −0.2, in which the slab is deflected by the transition, and little or no penetration occurs. Retrograde slab motion and trench migration occurred in nearly every case, with the overriding plate moving parallel to but faster than the trench, causing the gap between subducting and overriding plates to close with time. Prograde trench motion was never observed, and the trench remained stationary only in the extreme case (free ridge condition with equal upper and lower layer densities). These results suggest that the transient extension found in many back arc basins may be a direct consequence of the tendency for retrograde subduction and the amount of extension may be governed in part by the degree of slab penetration through the transition zone.

We have carried out a comparison study for a set of benchmark problems which are relevant for convection in the Earth's mantle. The cases comprise steady isoviscous convection, variable viscosity convection and time-dependent convection with internal heating. We compare Nusselt numbers, velocity, temperature, heat-flow , topography and geoid data. Among the applied codes are finite-difference, finite-element and spectral methods. In a synthesis we give best estimates of the 'true' solutions and ranges of uncertainty. We recommend these data for the validation of convection codes in the future.

Summary The time‐averaged geomagnetic field on the core–mantle boundary is interpreted using numerical models of fluid dynamos driven by non‐uniform heat flow. Dynamo calculations are made at Prandtl number Pr= 1, magnetic Prandtl numbers Pm= 1–2, Ekman numbers E= 3 × 10−4–3 × 10−5 and Rayleigh numbers 10–30 times the critical value for different patterns of heat flow on the outer boundary of a rotating, electrically conducting spherical shell. The results are averaged over several magnetic diffusion times to delineate the steady‐state magnetic field and fluid motion. When the boundary heat flow is uniform the time‐averaged flow approaches axisymmetry and the magnetic field is mostly a geocentric axial dipole (GAD). The largest departure from GAD in this case is the octupole field component. When the amplitude of the boundary heat flow heterogeneity exceeds the average heat flow, the dynamos usually fail. Lesser amounts of boundary heterogeneity produce stable dynamos with time‐averaged magnetic fields that depend on the form of the boundary heterogeneity. Elevated heat flow in the northern hemisphere produces a time‐averaged axial quadrupole magnetic field comparable to the inferred paleomagnetic quadrupole. Azimuthally periodic boundary heat flow produces a time‐averaged magnetic field component with the same azimuthal wavenumber, shifted in longitude relative to the heat flow pattern. Anomalously high and anomalously low magnetic flux density correlate with downwellings and upwellings, respectively, in the time‐averaged fluid motion. A dynamo with boundary heat flow derived from lower‐mantle seismic tomography produces anomalous magnetic flux patches at high latitudes and westward fluid velocity in one hemisphere, generally consistent with the present‐day structure of the geodynamo.