A history of the discovery and physical interpretation of Kimura's z-term is briefly reviewed. Z-term is now known as a manifestation of the dynamical response of the fluid outer core to. the periodic nutational (tidal) torque due to the Sun. Consequently, z-term is closely related in its nature with recent studies of the structure and dynamics of the core-mantle boundary region by means of the high-precision nutation observations with VLBI.

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High-pressure experiments suggest the possibility that liquid iron from the core may infiltrate the lower mantle oxides at grain boundaries thus creating heterogeneity at the grain scale. Lateral heterogeneity in seismic velocities, in the D" layer at the base of the mantle, exists at the scale of hundred kilometers. Various scenarios purporting to account for the seismic heterogeneities by infiltration are examined and found wanting. However, if it is assumed that convection can spread infiltrated material throughout the D" layer, it is possible to account for the observed decrease or increase in seismic velocities by about 1 vol% iron alloy at grain boundaries in the liquid or solid state respectively, depending on the depth of the isotherm corresponding to the melting point of the alloy.

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A new assessment of the thermodynamic properties of the lower mantle yields a more secure value than hitherto for the adiabatic Anderson-Griineisen parameter at a nominal depth of 1771 km, ∂_S=(∂In K_S/ ∂lnρ)=1/αvK_S(∂K_S/∂T)_P=2.4. The corresponding temperature dependence of rigidity is not well constrained but for the purpose of calculations is assumedd to be ε=1/αVμ (∂μ/∂T)_P=9.0. These values give the temperature dependences of seismic velocities (∂Inα/∂T)_P= -2.4×10^-5 K^-1, (∂Inβ/∂T)_P = -4.8×10^-5 K^-1. These temperature sensitivities are insufficient to explain reported lower mantle velocity anomalies without implausible temperature variations. Although temperature variations in the lower mantle must occur, tomographic observations do not provide direct evident for them, but are probably dominated by compositional variations. However, some correlation between composition and temperature may be expected, so that tomography may give still an indication of the pattern of the core-to-mantle heat flux.

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Birch was the pioneer of understanding the earth's core: that the core was mostly iron; that the solid inner core was nearly pure iron; that the liquid core had most of the impurities; and that the phase diagram (p.d.) of pure iron was complicated with several phases and triple points (t.p.). In 1972 he said, “5000°K, for the central temperature ... may have some standing as an upper limit.” I reconstruct the phase diagram accounting for new experiments and theories arising in the subsequent two decades. I stretch Birch's p.d. to account for the experiments of BOEHLER et al. (1990), BROWN and McQUEEN (B&M) (1982, 1986), and Yoo et al. (1992, 1993). BOEHLER (1993) reports the ε-γ-liquid t.p. at 100 GPa. This t.p. plus the solid-solid (ss) transition at 200 GPa reported by B&M require an additional high T phase, α', which has been suggested to be bcc. The new α' phase requires another t.p. near 190 GPa, which implies that the inner core is made largely of bcc iron. I suggest a T_m of about 6500°K for pure iron at the inner core-outer core boundary pressure. The T_m of the inner core itself will be affected by possible inner core impurities and by outer core impurities of larger concentration. To paraphrase Birch, 5700°K for the central temperature may have some standing as an upper limit.

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A possible whole-mantle convection model is employed to investigate the convection patterns and the topography of Core-Mantle Boundary (CMB) in this work. We choose three general boundary conditions and three special conditions to constrain our model. These are 1) the vertical velocity is equal to zero at both lower and upper boundaries and the temperature is constant at the upper boundary, 2) Runcorn's correlation equation between mantle convection and the Earth's geoid anomalies, 3) the horizontal velocity is equal to the poloidal component of Plate absolute motion model AM1-2 (MINSTER and JORDAN, 1978), 4) the correlation equation between mantle convection and a “rigid-boundary earth's” geoid anomalies predicted from density heterogeneity of the mantle transformed from the seismic tomography models LO2.56 (DZIEWONSKI, 1984) and M84C (WOODHOUSE and DZIEWONSKI, 1984). Results show that computed topography of CMB is changing with Rayleigh number. When the Rayleigh number of the mantle is taken in the region 50000-80000 (not more than 1.5 times critical) the peak-to-peak value of CMB topography is about 5.6-6.2 km. The predicted map of CMB topography can fit the observed results constructed by inversion of PcP residuals very well (MORELLI and DZIEWONSKI, 1987). It is clear that there are highs extending over the Central and Eastern Pacific, and three lows appear in the regions: south of Japan, Colombia, and North-east of New Zealand in both maps.

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J-Array is a large-aperture short-period seismic array extending over the whole Japan with its dimension. being 3000 km in length and 300-500 km in width. It counts 218 stations. The recording system and the present status of J-Array program are presented in detail. Array analyses of a large volume of seismic waveform data recorded at J-Array enable us to detect even small-amplitude seismic waves refracted, reflected, converted or scattered at seismic velocity discontinuities or inhomogeneities existing in deep portions of the Earth, which convey information on the detailed structure and the regional variation of the central core, the lower mantle and also the upper mantle.

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We analyzed digital waveform data recorded at J-Array, a large-aperture short-period seismic array in Japan, in order to search for P-waves reflected and/or refracted at a velocity discontinuity possibly existing at the top of D" layer. During the period of April 1991-June 1992, we selected waveform data with good quality for 8 events; 3 events in California-Nevada, and 5 events in Fiji-Tonga-New Zealand. They are located in the distances of 70 ti 85° from the J-Array, where the phases originating at D" layer are expected. However, the P-waves from the events display no clear later arrivals with corresponding slowness in the raw paste-up traces. In slant-stacked records from two events of Fiji Islands, there is a small peak with slowness and delay corresponding to waves originating at D" layer although these peaks are not so prominent. For the other events, we could not observed the phases even in the stacked records. Comparing synthetic data with observed ones, there can exist a P-wave velocity discontinuity with a jump of 1.1∼1.6% at the top of the D" layer beneath the paths from. Fiji Islands to Japan. However, the data set is only for the period of a year and we might need more good quality data for complete analyses.

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Travel times of long-period SKS and S2KS phases recorded at the GDSN and WWSSN stations were analyzed to retrieve information about the radial structure of the outer core. We propose a new velocity model for the outermost core named KTH. The velocity at the top of the core is 8.016 km s^-1, and the velocity in the outermost 200 km of the core is 0.11 km s^-1 faster than that. of HALES and ROBERTS (1971), that in the outer 200∼400 km of the core is identical within 1% to that of HALES and ROBERTS (1971). We find that the inhomogeneity index η is slightly larger than unity in the outermost 100∼200 km of the core where a preferable value of η just beneath the core-mantle boundary is 1.5 which corresponds to Brunt-Väisälä frequency N of 8.6 × 10^-4 s^-1. We suggest that the outermost 100∼200 km of the core is stably stratified. The thickness of the stable stratified layer in the present study is not far from those of 70∼80 km thickness derived from theoretical considerations. By comparing possible lateral heterogeneity in the outermost core with temperature distribution from a geomagnetic study, we infer that a chemically stratified layer is preferable in the outermost core.

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From the various presently discussed coupling mechanisms of core and mantle the topographic coupling along the core-mantle boundary (CMB) is considered in detail. A new estimation of this coupling is given which is based on exact asymptotic analysis of corresponding hydrodynamical equations. It is shown that for the model without dissipation, topographic coupling between the core and mantle is probably much larger than previously estimated. Effects of vortical flow dissipation are considered.

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Zonal modes of mantle deformation may couple with the Earth's rotational motion. Increases of the LOD (slowing down of the Earth's rotational speed) suggest a coupling with increases of the vertical in the low latitude zone. This relation may be due to the angular momentum redistribution in the mantle associated with motions in the fluid core. Thermal core-mantle interaction is proposed to explain the coupling between the fluid motion near the CMS and the elastic mantle in a simple model valid at the equator near the CMB. Transport of mass in the fluid core near the CMB along the north direction can be large enough to explain the observed values of the variation of the vertical.

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The variations of the length of day and the angular velocity of the relative rotation of the Earth's core derived from geomagnetic secular variation were compared from 1650 to 1985. Periods comparable with the well-known 60 to 70-years periods of the fluctuations in the Earth's rotation could be found within the spectrum of the core rotation parameters by lengthening of the previously used time series to epochs before 1900. Additionally, the torques of the geomagnetic core-mantle coupling were computed for this time interval. The results agree with previously derived values for epochs after 1900. The coupling behaves like a homogeneous and isotropic magnetic friction, and the difference between axial and equatorial mechanical torques derived from Earth rotation parameters cannot be explained by magnetic core-mantle coupling.

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We review recent theoretical and numerical advances which allow the accurate calculation of modes of oscillation of the Earth's liquid core with periods beyond the range of acoustic radiation effects. In particular, the forms of the governing equations and boundary conditions at long periods, the use of effective internal Love numbers, and variational methods for the calculation of core modes, are considered. The Product Spectrum is introduced as a method of comparing, in the frequency domain, common features of gravity records taken at different observatories and at different times. It is applied to four long superconducting gravimeter records from Brussels, Bad Homburg and Strasbourg totalling more than 111, 000 hours of observations. A method of detection and identification of core oscillations, based on rotational splitting, is presented and applied to three resonances found in the subtidal band of the European Product Spectrum. While the central frequencies of these resonances are in excellent agreement with the resonant frequencies for the translational modes of the solid inner core, computed ignoring its inertial drag, the two equatorial modes are oversplit compared to observation when computed in the conventional free oscillations approximation, which includes inertial drag, but ignores other important dynamical effects such as viscous drag and the Ekman, and possibly, the Ekman-Hartmann, boundary layer surrounding the inner core. Recent results from an improved fully dynamical theory of the translational oscillations. are described. The problem of the detection and identification of other core modes, particularly those in the intertidal band, is discussed.

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Previous work has shown that the surface gravity effect associated with core modes (undertones) for a non-rotating Earth model is at or below the nanogal level of detectability for a large earthquake excitation. The assumption in the non-rotating case is that each undertone consists of a single spherical harmonic. In this study we add the Coriolis force to the equations governing the oscillations in a rigid shell with the Boussinesq approximation. By including up to 20 additional harmonics, we find that there are many solutions that are still dominated by low-degree spherical harmonics when judged by the distribution of kinetic energy among the harmonics. For these modes the contribution of higher degrees to the eigenfunctions is not substantial, which suggests that the addition of rotation will probably not significantly change the gravity effects computed without rotation. This conclusion remains tentative until verified in a fuller treatment that explicitly evaluates the excitation for a rotating Earth model.

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We describe the superconducting gravimeter (GWR #11) observation system at Kakioka and present initial results. The observed raw gravity data contain the tidal signal, stepwise changes, drift, etc. The tidal gravity values were examined by the tidal analysis program, BAYTAP-G. A calibration factor for the GWR #11 gravimeter of 51.2486 μGal/volt was determined by comparison between the observed M₂ gravimetric factor and the theoretically calculated one. The other gravimetric factors and phases observed are coincident with theoretically calculated ones to within 100 nGals. Stepwise changes occurred due to large, nearby earthquakes and a kind of deformation mechanism of the instrument and/or a newly constructed U shaped concrete pillar on which the gravimeter is supported. Long term drift can be represented by the sum of two exponential curves with two different decay constants, 35 days and 609 days, indicating that two types of creep processes may be occurring in the gravimeter or in the supportive pillar. The gravimetric factor of polar motion was determined as 1.35±0.20 using the gravity residuals together with the instantaneous rotation axis position data from the IERS network. This value suggests that changes in gravity due to polar motion are probably affected by the atmosphere and mantle anelasticity.

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Search for evidences of the dissipative core-mantle coupling is probably the most interesting subject for VLBI Earth rotation observations in view of physical informations to be obtained about the core-mantle boundary region. It is shown that the VLBI detected out-of-phase component of the retrograde annual nutation term is most likely to be a manifestation of the dissipative coupling because the coupling coefficient required to explain the observed out-of-phase component is just in the same order of magnitude as the one associated with the decade fluctuations in the rotation rate of the Earth, which are commonly attributed to the dissipative core-mantle coupling. Several observational tests are proposed to clarify the mechanism and frequency characteristics of the coupling. Researches along this direction require accuracy and time resolution of the VLBI observations beyond their present-day level. It is shown that a VLBI system of new design, 'antennacluster-antennacluster VLBI system', will be able to realize the high performance required.

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Differential VLBI technique can measure the variation in the angular distance between two artificial radio transmitters on the Moon with an accuracy of a few centimeters. We can observe the physical librations of the Moon through this technique since rotation of the Moon changes the angular distance. The gravitational field of the Moon can also be determined by observations of the angular distance between the radio source on the Moon and that on a lunar orbiter. Calculations show that this technique can determine the amplitude of the physical librations with an accuracy of 10^-5 which are one or two orders higher than those obtained by using the Apollo Lunar Surface Experiments Package in 1970's. We can estimate the density and the radius of the lunar core through accurate amplitude and period of the librations together with seismic observations. The accuracy of determination of the lunar gravity harmonics of degree 2 derivable from the VLBI observations are in the range from 10^-4 to 10^-6. We are developing radio transmitters which will be put on the lunar surface by hard landing from the lunar orbiter.

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Deep magnetovariational soundings have been carried out using the data of the geomagnetic observatory net and the MAGSAT satellite. Complex apparent resistivities estimated from satellite data by two independent methods are found to be in accordance with numerous mean values obtained only from ground data. Assuming the spherical symmetry of the Earth's layers the interpretation in the parametric models class of joint results has been done. The global estimation of the electrical conductivity structure of the Earth's mantle indicates the presence of a high conductivity layer about 200 km thick at a depth of approximately 600-700 km.

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Several years ago I discovered an intriguing spatial correlation between plate motions and variations in the strength of the geomagnetic field with the major lithospheric plates tending to move from areas where the magnetic field is diminished to where it is enhanced (GOODACRE, 1987). One implication of this visual correlation is that there is a link between the pattern of fluid motion in the Earth's outer core and the convection of material in the mantle. In order to estimate the motion of fluid in the outermost portion of the core, we require a knowledge of not only the magnetic vector potential, A, and its time variation, but also the scalar electrostatic potential, Ψ. Under the assumption that there is no large, time-varying toroidal magnetic field in the Earth's core I have calculated smooth representations of the induced electric field intensity, -∂A/∂t, the electrostatic field intensity, -∇Ψ, and the motional electric field intensity, v × B, needed to generate electric currents which reproduce the Earth's magnetic field and its secular variation. Superimposed on a postulated main meridional flow consisting of fluid upwelling at the equator and downwelling at the poles is a secondary flow system in which fluid spreads out from a point beneath the triple junction of the South American, African and Antarctic lithospheric plates, travels in a thin layer at the surface of the core and then descends in the vicinity of Indonesia. Except in the region of the south Atlantic Ocean, the inferred secondary flow of fluid in the outermost core tends to mimic the directions in which the major lithospheric plates move with respect to “hot spots” thereby supporting the idea that most of the major features of the non-dipole portion of the geomagnetic field are caused and controlled by mantle convection and remain “stationary” on an historic time scale.

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The core-mantle boundary below the Pacific is one of the most interesting regions for the study of the Earth's core because of the phenomena which seem to be characteristic to this region. The geomagnetic phenomeno is one of them. Two features are widely believed to exist in the geomagnetic field in this region. One is absence of the non-dipole field, and the other is its small secular variation, which might be related to special structures of the core-mantle boundary region below the Pacific. This paper re-examines historical data of declination, and suggests that an intense focus of the non-dipole field existed in the North Pacific in the 17th century, and concludes that the absence of the non-dipole field as seen at present has not been a permanent feature of the magnetic field in the Pacific, implying that the Pacific region is no special region in this sense.

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Global features of the geomagnetic field over the past 10, 000 years were studied. Reliable data set of inclination and declination at twelve localities were prepared by combining paleomagnetic data with archaeomagnetic data. We estimated the time variation of the geomagnetic dipole moment by analyzing the virtual geomagnetic pole (VGP) positions calculated from this data set. The geomagnetic poles were calculated for every 100-year interval by averaging the VGP. The distribution of the geomagnetic poles has an elliptic shape and westward movement was predominant throughout the interval. The obtained time sequence of the movement of the geomagnetic pole can be divided into three intervals: during the period between ca. 7000 and ca. 3700 B.P. (B.P.: before 1950 A.D.), the movement of the geomagnetic pole was inactive, and it was active before and after this period, fluctuating over 10 degrees. Continuous time variation of the dipole moment was inferred from the angular dispersion of the VGP, by investigating the relationship between the angular dispersion of the VGP and the dipole moment. The result suggests that the dipole moment had sharp peaks of high intensity around .8500 B.P., 4200 B.P. and 1200 B.P.

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Fluid motion caused by flotation of fine immiscible particles is investigated. Fine immiscible particles can be formed by several mechanisms in the Earth's outer core. For example, light materials may exsolve from cooling iron melt. Light-material-rich blobs may be formed through a boundary layer instability, even if light materials are thermodynamically miscible with molten iron. Governing equations for two-phase flow composed of fine particles and ambient fluids are derived from the conservation laws of mass and momentum. The stationary state without macroscopic fluid motion is neutrally stable to an infinitesimal disturbance. Transient fluid motion is induced by a horizontal disturbance of particle concentration. The resultant fluid motion can be classified into three types. One is a circulative motion driven by the buoyancy of fine particles and the others are non-circulative flows caused by “apparent compressibility” of two-phase flow. If we took into account effects of nonlinear advection, the buoyancy-driven flow would be self-sustaining. The relationship between the flow types and values of nondimensional parameters are investigated. The parameter range where the buoyancy-driven motion is observed is approximately given by G > 3Q² and G > 30Q. G and Q are the nondimensional parameters defined as G ≡ ρδH³g/η² and Q ≡ Δv_z ρH/η, where ρ, η, δ, H, Δv_z and g are the density and viscosity of mixture, the difference of intrinsic density between particles and the ambient fluid, the depth of the fluid layer, the ascending velocity of particles relative to the motion of ambient fluid, and the gravitational acceleration, respectively. The lower the relative velocity of ascending particles is, the more effectively the circulative motion occurs. The values of physical parameters estimated for the outer core fall in the range in which a buoyancy-driven motion should be observed.

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An attempt is made to derive fluid motion in the Earth's outer core from geomagnetic field data. We implicitly incorporate the energy source for the geodynamo in the prescribed radial dependence of poloidal velocity field. Then the Navier-Stokes equation for the toroidal constituent and the induction equation for the toroidal and the poloidal magnetic fields are solved so as to fit the magnetic field at the core-mantle boundary estimated through downward continuation on the assumption that the mantle is an insulator. The basic standpoint is that the large-scale magnetic field is maintained by induction processes associated with large-scale fluid motion within the core. We also impose the condition that time variations of the velocity and the magnetic fields are very slow. The generation balance in the induction equation, for the derived velocity and magnetic fields, suggests that the geodynamo is likely to be of α²ω-type.

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We perform a simple linear analysis of the response of the outer core fluid to a sectorial temperature heterogeneity at the core-mantle boundary (CMB). The locations of upwellings and downwellings are shown to be controlled by the Elsasser number. When the Elsasser number is less than the order of unity, upwellings occur to the east of hot regions, and downwellings occur to the west of hot regions. When the Elsasser number is more than the order of unity, upwellings occur beneath hot regions, and downwellings occur beneath cold regions. Our theory provides an explanation for the correlation between the observed magnetic feature and the lateral heterogeneity of the seismic velocity in the lower mantle, which would correspond to the temperature heterogeneity at the CMB. From the correlation, we infer that the Elsasser number is a little less than unity in the Earth's outer core. Moreover, we investigate whether the resulting flow can sustain dynamo action or not. A temperature heterogeneity of the order of 10^-6 K over a length scale of 10³ km would be sufficient for the generation of dynamo action.

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The dynamics of the stably stratified layer at the top of the core, which we call the H-layer or the hidden ocean of the core (HOC), is considered. It is shown that global axisymmetric eigenoscillations of the H-layer are possible that are similar to MAC-waves. These oscillations have periods of the order of a few decades (∼65 yr) if N ∼ 2Ω where N is the Brunt-Väisälä frequency of the H-layer and Ω is the frequency of the Earth's rotation. H-layer oscillations can be excited by an instability mechanism that resembles baroclinic (sloping) instability, and they in turn can excite torsional oscillations (TO) in the bulk of the core. The joint action of these two oscillations provide a mechanism for the generation of the decade geomagnetic secular variations, and the associated variations in the length of day. Rough estimates of the physical parameters of the H-layer are obtained by comparison of the HOC-oscillation theory with observations. The existence of the H-layer has significant consequences for the Earth's dynamo, that are briefly discussed.

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This is an attempt to understand better the dynamics of the small-scale compositionally buoyant flow in the Earth's core which may be responsible for the generation of the Earth's magnetic field by dynamo action, by determining the rise law and the flow structures of a buoyant rigid cylinder rising in a rotating electrically conducting fluid in the presence of a large-scale magnetic field. The problem is linearized by assuming small Rossby and magnetic Reynolds numbers, and the Lorentz force is assumed to be larger than the viscous and Coriolis forces. It is found that the rise speed is larger than one would expect from simple scaling arguments. This rapid speed is related to the large-scale flow structures, elongated in the direction of the applied magnetic field, which carry the electric currents associated with the Lorentz force. This elongation serves to weaken the Lorentz force such that the force balance within these structures is magnetostrophic (between Coriolis and Lorentz). The restriction to the case of a rigid cylinder makes this study directly applicable only to the polar regions of the outer core.

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A multiple-scale asymptotic technique is used to study the propagation of slow hydromagnetic waves in a magnetostrophic regime for an incompressible, inviscid, perfectly conducting fluid of constant density in rotating cylindrical geometry. Such waves may play an important role in both the generation and behavior of the Earth's magnetic field. Knowledge of their behavior may be useful in studying the flows at the core-mantle boundary. The equations of motion are linearized about an ambient state of no motion with respect to rotating cylindrical coordinates and an azimuthal ambient magnetic field of the form r^n/2 where r is the radial distance in cylindrical coordinates. The waves may be trapped in a variety of ways while westward travelling modes may be unstable for n > 3 . These results extend the local results of ACHESON (1972) and are consistent with the numerical results of FEARN (1983).

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A general asymptotic procedure is suggested for describing the magnetohydrodynamic (MHD) flows in the outer core of the Earth on a time scale larger than 100 years. The asymptotic expansion is based on the small Ekman number in the Earth's outer core. Fluid motion in the core can be divided into two parts: large-scale flows in the bulk of the outer core and small-scale ones concentrated near the boundaries. The small-scale and large-scale flows are consistent with each other, when the ratio of small-scale electric currents to large-scale ones and the ratio of Coriolis to Lorentz forces in the bulk of the outer core are roughly described by the magnetic Reynolds number. The present configuration of the Earth's magnetic field requires a boundary layer beneath the core mantle boundary (CMB) which is much thicker near the equator than at other latitudes. The small-scale electric currents in this layer can produce geomagnetic secular variations. Through the application of the present theory to axisymmetric flows, it is shown that the description of the fluid flow is less complicated with the presence of the magnetic field than is in the purely hydrodynamic case. The MHD coupling removes most of complications associated with the formation of the boundary layers.

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In turbulent dynamos, an a-effect is assumed, which is related to the helicity of the fluid motion and effectively generates the magnetic field. In the case of laminar dynamos, there is no a-effect term, but the helicity associated with the laminar flow exists. We examine if this helicity works similarly to that of the turbulent motion. We first seek the velocity field which generates the largest helicity. In the class of flows that have the same kinetic energy, and whose toroidal and poloidal radial functions are zero at the surface, we show that Beltrami flow correspond to local maxima of the mean helicity. However there is no absolute maximum for the mean helicity in that class of flows. Next we calculate some laminar kinematic dynamo models using this flow, notably s₂^2c + t₂^2c + t₂^2s combination modified from PEKERIS et al. (1973). The numerical results show that the larger the mean helicity becomes the more efficient the dynamo becomes. We also show that dynamo process cannot be sustained with the velocity s₂^2c + t₂^2s, which has no net helicity and corresponds to the case for which the generation term Γ of BRAGINSKY (1964) becomes zero. In these calculations we examined not only the models starting from the axial dipole (S₁) but also those starting from other harmonics, and we find that the models starting from equatorial dipoles (S₁^1c and S₁^1s) have the smallest critical Reynolds number among the dynamos which is sustained by the velocity S₂^2c + t₂^2c + t₂^2s.

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Time evolution of the magnetic field is examined numerically for some models of thermally driven MHD dynamo in a spherical shell. Special attention is paid to whether the polarity of the dipole magnetic field, in the models, reverses its sign during time evolution. Here we present the results for two typical models. In one model, the temperature is held constant at both boundaries of a spherical shell, whereas in the other, the distribution of temperature is represented by the degree 2 and order 2 constituent of spherical harmonics. The former shows an oscillatory variation and hence the polarity is reversed rather periodically. The latter results in a rather stationary state and the magnetic field tends to stay at one polarity state. These numerical results imply that the thermal interaction between the core and the mantle can control the frequency of reversal.

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We describe a nonlinear, axisymmetric, spherical-shell model of a planetary dynamo. This intermediate-type dynamo model requires a prescribed helicity field (the alpha effect) and a prescribed buoyancy force or thermal wind (the omega effect) and solves for the axisymmetric time-dependent magnetic and velocity fields. Three very different time dependent solutions are obtained from different prescribed sets of alpha and omega fields.

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