Philippe Machetel

Convection within the inner-core and thermal implications

Estimation of the Rayleigh numbers of the inner-core leads to the conclusion that, even with low internal heating rates, this region of the Earth is convecting. This work presents an axisymmetrical model able to investigate convection in a sphere and its applications to the Earths inner-core. Rayleigh numbers ranging from the critical (onset of the convection) to ten thousand times the critical have been explored. The thermal implications of a convecting inner-core have been pointed out: in all the cases the temperature profiles are very close to the adiabat, leading to the possibility of a partially molten regions in the inner-core. Indeed, the most important effects appear in the first tens of kilometers, just below the inner-core surface and could be at the origin of the low quality factors Qα and Qβ revealed by seismological studies.

Chaotic axisymmetrical spherical convection and large-scale mantle circulation

Abstract This paper presents a study of high Rayleigh number (up to 200 times supercritical) axisymmetrical convection in a spherical shell with an aspect ratio relevant for the Earths lower mantle. Both bottom-heated and internal heated cases have been considered. Computations have been carried out for an infinite Prandtl number isoviscous fluid with free slip isothermal boundary conditions. The first part of the paper is devoted to the influence of the resolution on the accuracy of the numerical results. It is shown that the resolution strongly influences the onset of time dependence. Recent methods of non-linear physics have been used to prove that the time dependence and the chaotic behaviors of the solutions are real ones. From these results we can confirm that convection is chaotic, in this particular geometry, even for Rayleigh numbers 200 times critical. Aperiodic boundary layer instabilities are found to be incapable of breaking up the large-scale flow, owing to the shear of the global circulation. Spectral analysis of the power associated with the thermal anomalies shows that there is an upward cascade of energy, due to small-scale chaotic instabilities, from l = 2 to l = 4–6 at the bottom boundary, in agreement with new seismic observations at the core-mantle boundary [1–3].

Spectral and geophysical consequences of 3-D spherical mantle convection with an endothermic phase change at the 670 km discontinuity

Abstract Numerical computations of 3-D compressible convection have been conducted in a spherical Earths mantle with an endothermic phase change at the 670 km discontinuity. The results validate the trends of layering of mantle convection induced by the phase change. Indeed, partial layering and two-layer convective circulation prevail for the same value of Clapeyron slope as was observed with an axisymmetrical approach. These 3-D results show that as far as the purely 3-D effects of convection are not concerned, the 2-D geometry allows relevant conclusions; in particular, on the cylindrical shape of the avalanches of upper-mantle material into the lower mantle which were observed at the poles of the axisymmetrical numerical simulations. However, the 3-D simulations allow direct computations of the geophysical consequences of mantle flows as thermal anomalies, topographical deflections of the bottom, upper and internal surfaces and the resulting geoid anomalies. Two-layered or intermittently layered convection induces geophysical anomalies that are in qualitative agreement with the real geophysical date. Whereas surface topographies computed from one-layer convection models or whole-mantle circulation models are too large compared with observations, it is possible to generate a satisfactory geoid and topography when a realistic phase change is considered at the 670 km discontinuity. This property is verified both for a layered and an intermittently layered structure of convection in the Earths mantle.

Infinite Prandtl number spherical-shell convection.

This work presents an overview of numerical simulations of thermal convection for constant viscosity, infinite Prandtl number fluids in a spherical shell, with mantle convection being the main application. Using high-resolution grids on a supercomputer Cray-2, we have monitored the transitions from steady state to the onset of oscillatory time-dependent convection. This occurs at a Rayleigh number which is around 30 times the critical for an inner to outer radii of.62. Additional bifurcations are found with increasing strength of convection. This process culminates in chaotic convection. Analysis of the spatial correlation function of the time-dependent signals shows that the dimensionality of this chaotic attractor, at about 60 times the critical, is around 2.8 and resembles a low dimensional fractal. A large scale circulation, dominated by the degree n =2 component, is found to coexist with aperiodic boundary layer instabilities, mainly starting from the bottom. Spectral analysis of the power associated with the thermal anomalies reveals an upward cascade of energy from n=2 to n=4 to 6 at the bottom boundary. This last signature agrees well with recent seismic findings at the core-mantle boundary.

Cretaceous length of day perturbation by mantle avalanche

Abstract These last 10 years, numerical models of mantle convection have emphasized the role of the 670 km endothermic phase change in generating avalanches that trigger catastrophic mass transfers between upper and lower mantle. On the other hand, scientists have emphasized the concomitance of large-scale worldwide geophysical and tectonic events, which could find their deep thermal roots in the huge mass transfers induced by the avalanches. In particular, the paleontological records show two periods of length of day (l.o.d.) shortening between 420 and 360, and 200 and 80 Myr BP. This last event is synchronous with a strong true polar wander and a global warming of the upper mantle. In order to study the potential effects of the avalanche on the main component of the Earth’s rotation, the Liouville equation has been solved and the l.o.d. evolution has been calculated from the perturbations of the inertia tensor. The results show that the inertia tensor of the Earth’s is mainly sensitive to the global transfers through the 670 km discontinuity. The l.o.d. perturbations will be synchronous with the global thermal effects of the avalanche. These theoretical results allow proposing a self-consistent physical mechanism to explain periods of the Earth’s rotation acceleration. Within this context, the l.o.d. shortening during the Cenozoic and Cretaceous brings one more clue to the possible participation of a mantle avalanche in generating the concomitant large scale events which have occurred during this very particular period of the Earth’s history.

Slab weakening by the exothermic olivine‐spinel phase change

Numerical modelling of mantle convection, with lateral variations of viscosity, and both the 670 km depth endothermic and the 400 km exothermic phase changes, reveals that downwellings are weakened upon crossing the exothermic phase change. A high temperature/low viscosity section is developed within the downgoing current, owing to both the olivine to spinel phase transition and the slowing down of the flow due to the 670 km endothermic transition. This mechanism may cause the creation of a weak zone at 400 km that results in a preferential location for horizontal or vertical slab tearing as revealed by seismic gaps in many slabs.

Global thermal and dynamical perturbations due to Cretaceous mantle avalanche

The numerical models of mantle convection agree to depict avalanches behaviour according to the level of endothermicity of the spinel → perovskite phase change. Their potential effects on the global thermal and dynamical states of the mantle have been computed thanks to a numerical code, which takes into account both the 400-km exothermic and the 660-km endothermic phase changes. The cycle followed by the avalanches is: local layering, destabilization of the 660-km thermal layer, travelling and spreading on the core, and reappearing of the local layering. Therefore, mantle convection is characterized by quiet periods of partial layering embedded in catastrophic events. During the avalanche, the amplitude of the surface velocity is multiplied by two, which would imply an enhanced plate tectonic and ridge activities. The global thermal effects of the avalanche are compatible with a high mantle temperature and an acceleration of Earths rotation during the Cretaceous. They also offer a coherent explanation to locate the origin of mantle plumes both within the CMB and just below the transition zone.The numerical models of mantle convection agree to depict avalanches behaviour according to the level of endothermicity of the spinel → perovskite phase change. Their potential effects on the global thermal and dynamical states of the mantle have been computed thanks to a numerical code, which takes into account both the 400-km exothermic and the 660-km endothermic phase changes. The cycle followed by the avalanches is: local layering, destabilization of the 660-km thermal layer, travelling and spreading on the core, and reappearing of the local layering. Therefore, mantle convection is characterized by quiet periods of partial layering embedded in catastrophic events. During the avalanche, the amplitude of the surface velocity is multiplied by two, which would imply an enhanced plate tectonic and ridge activities. The global thermal effects of the avalanche are compatible with a high mantle temperature and an acceleration of Earths rotation during the Cretaceous. They also offer a coherent explanation to locate the origin of mantle plumes both within the CMB and just below the transition zone.

New Perspectives on Mantle Dynamics from High-resolution Seismic Tomographic Model P1200

Recently a high-resolution tomographic model, the P1200, based on P-wave travel times was developed, which allowed for detailed imaging of the top 1200 km of the mantle. This model was used in diverse ways to study mantle viscosity structure and geodynamical processes. In the spatial domain there are lateral variations in the transition zone, suggesting interaction between the lower-mantle plumes and the region from 600 km to 1000 km. Some examples shown here include the continental region underneath Manchuria, Ukraine and South Africa, where horizontal structures lie above or below the 660 km discontinuity. The blockage of upwelling is observed under central Africa and the interaction between the upwelling and the transition zone under the slow Icelandic region appears to be complex. An expansion of the aspherical seismic velocities has been taken out to spherical harmonics of degree 60. For degrees exceeding around 10, the spectra at various depths decay with a power-law like dependence on the degree, with the logarithmic slopes in the asymptotic portion of the spectra containing values between 2 and 2.6. These spectral results may suggest the time-dependent nature of mantle convection. Details of the viscosity structure in the top 1200 km of the mantle have been inferred both from global and regional geoid data and from the high-resolution tomographic model. We have considered only the intermediate degrees (l= 12–25) in the nonlinear inversion with a genetic algorithm approach. Several families of acceptable viscosity profiles are found for both oceanic and global data. The families of solutions for the two data sets have different characteristics. Most of the solutions asociated with the global geoid data show the presence of asthenosphere below the lithosphere. In other families a low viscosity zone between 400 and 600 km depth is found to lie atop a viscosity jump. Other families evidence a viscosity decrease across the 660 km discontinuity. Solutions from oceanic geoid show basically two low viscosity zones: one lying right below the lithosphere; the other right under 660-km depth. All of these results bespeak clearly the plausible existence of strong vertical viscosity stratification in the top 1000 km of the mantle. The presence of the second asthenosphere may have important dynamical ramifications on issues pertaining to layered mantle convection. Numerical modelling of mantle convection with two phase transitions and a realistic temperature- and pressure-dependent viscosity demonstrates that a low viscosity region under the endothermic phase transition can indeed be generated self-consistently in time-dependent situations involving a partially layered configuration in an axisymmetric spherical-shell model.

A thermomechanical numerical model for crustal accretion of medium to fast spreading mid-ocean ridges

We propose a new thermomechanical numerical model of mid-ocean ridge accretion aimed at investigating asymmetric spreading rates, diverse configurations of lens and sill magma injections, crystallization and depth, and on- and off-axis patterns of hydrothermal cooling. The numerical algorithm iteratively resolves temperature and motion equations until it reaches a stationary solution. The motion equation was written in a vorticity-stream function formalism, with boundary and internal conditions applied to the stream function to impose the style of magma injection. Unlike in previous models, our model does not assume an a priori shape for the temperature field, which is initiated by an initial half-space cooling according to the left and right spreading rates. Complex patterns of hydrothermal cooling are simulated by enhanced thermal diffusivity. The model succeeds in describing the dynamic and thermal effects of spreading rates, the style of magma intrusion, and the hydrothermal cooling. Accurate descriptions of these are essential to study the cooling histories of crustal rocks and geophysical observables.

Evaluation of First Order Error Induced by Conservative-Tracer Temperature Approximation for Mixing in Karstic Flow

formalism has been used to conduct a several orders of magnitude parametric exploration based on the Peclet and the Reynolds numbers. The final errors, between the AW and CW configurations, remain less than 1% over all of the parametric range. The combination of error curves bounds a closed volume in error space that gives a first upper bound of the error made by considering the temperature as a conservative tracer. Applying the method to an illustrative example of karst allows us to reach a first order error within a few degrees °C.