L. Cserepes

3D convection at infinite Prandtl number in Cartesian geometry — a benchmark comparison

Abstract We describe the results of a benchmark study of numerical codes designed to treat problems of high Prandtl number convection in three-dimensional Cartesian geometry. In addition, quantitative results from laboratory convection experiments are compared with numerical data. The cases of bimodal convection at constant viscosity and of square cell convection for temperature-dependent viscosity have been selected.

Numerical studies of non-Newtonian mantle convection

Abstract Numerical model computations have been carried out to determine how the stress-dependence of non-Newtonian viscosity affects the flow structure of thermal convection. The viscosity laws have been chosen in accordance with present knowledge of upper mantle rheology, based on the diffusion and dislocation creep laws of olivine. The results show that there are important differences between the structures of Newtonian and non-Newtonian convection. While the Newtonian models are insufficient in some respects, the non-Newtonian solutions can explain the characteristics of the real mantle flow. However, this may require a faster plastic deformation than power law dislocation creep, at least in the high-stress regions of the mantle, e.g. at the active plate margins.

Dynamical consequences of mid‐mantle viscosity stratification on mantle flows with an endothermic phase transition

Recent geophysical evidences from seismology and geoid inversions have pointed out the existence of some layering between 900 and 1000 km depth and the possibilities of a low viscosity zone between 660 and 1000 km depth. Using a finite-difference and spectral code, we have conducted 3-D calculations of thermal convection with the endothermic phase transition at 670 km depth and a family of viscosity profiles with emphasis on the presence of two low viscosity zones, one in the upper mantle between 100 and 250 km depth and the second one between 670 and 1000 km depth. Below 1000 km the viscosity increases with depth. The surface Rayleigh number used was in the range of 10 7 . The dominating effect is that due to the second low viscosity zone below the phase change. Layered convection is induced by the presence of this second asthenosphere, which causes horizontal flow to develop in there. Alternatively, a viscosity increase at 670 km depth would shift convection to the single-layer regime. The potential sharp variations of the viscosity structure between 670 and 1000 km depth can greatly influence the global flow dynamics of the mantle.

Effect of the mid-mantle viscosity and phase-transition structure on 3D mantle convection

Abstract Recent geophysical evidence shows some sort of layering in the lower part of the mantle transition zone down to a depth of 1000 km. Seismic observations have revealed a sharp reflector surface at around 900 or 1000 km depth for which a possible explanation can be given in terms of a new phase transition of the lower-mantle constituent minerals. Furthermore, new results from the inversion of the oceanic geoid show the existence of a second low viscosity zone (LVZ) somewhere between 660 and 1000 km depth. The existence of the second LVZ may be linked to the mid-mantle phase transitions. The phase and viscosity stratification of the transition zone have been included in a series of 3D convection simulations in a 4×4×1 rectangular box with a surface Rayleigh number of 2×10 7 . Beneath the well-known 400 and 660 km phase changes, we assumed a hypothetical weak endothermic transition at 1000 km in some of our models. The principal controlling factor of the style of mantle convection is still the 660 km endothermic transition, which sets up a partial or full barrier to flow, causing stratified circulation. We used various viscosity profiles with emphasis on the model containing the second LVZ. The main consequence of this zone is to enhance flow layering. Many plumes can emanate from the transition zone and small-scale instabilities develop in the second LVZ. When the 1000 km endothermic phase transition is included, these instabilities can grow only at a few places but then they form strong downwellings. Two distinct types of penetrative, deep downwellings can be present at the same time: one which crosses the whole transition zone, and another one which crosses only the 660 km discontinuity and stops at 1000 km at least temporarily. This can explain seismological observations which suggest that subducted slabs can be retarded not only by the 660 km boundary but also by some deeper obstacle near 1000 km depth.

Effect of depth‐dependent viscosity on the pattern of mantle convection

Three-dimensional structures of thermal convection are studied by numerical experiments in a rectangular domain of a plane fluid layer. The main question is the joint effect of the heating mode and the depth-dependent viscosity on the planform of the circulation. Heating mode is defined by the ratio of internal and basal heat inputs. For viscosity-depth functions, simple models of the mantle viscosity are used. If the Rayleigh number is of the order 105–106 (based on the maximum viscosity), this choice produces cellular flow with a closed network of cold descending sheets around isolated upwellings, independently of the heating mode. The central upwellings are concentrated in narrow cylindrical plumes if there is a significant basal heat input. Convection of the Earths mantle may occur with descending currents represented by subduction and ascending currents in the form of plumes situated below hotspots.

Mesoscale structures in the transition zone: Dynamical consequences of boundary layer activities

Recent geophysical evidence from seismology, mineral physics, viscosity inversion shows that the mantle between 400 and 1000 km is extremely complicated, with intermediate scale structures present regionally as seismic reflectors under the 660 km discontinuity and bent plume-like structures under the transition zone. We have studied the dynamics of the transition zone with two models, an axisymmetric spherical-shell (2-D) model with a horizontally averaged temperature- and pressure-dependent viscosity and a 3-D Cartesian model with a depth-dependent viscosity. Two mantle phase transitions have been employed in both models. Results of the 2-D axisymmetric model show that the interaction of the lower mantle plumes with the transition zone can result in a horizontal channel flow right underneath the 660 km and in the birth of secondary plume some distance away from the lower mantle plume. The strength of the secondary plume increases in strength with larger viscosity contrast across the 660 km discontinuity. In the 3-D model we have found that with the presence of a second low viscosity zone somewhere between 660 and 1000 km, many secondary instabilities are developed in the second asthenosphere and the mesoscale thermal structure developed can become quite complex. Many small-scale plumes can emanate from the transition zone. Occasionally a very large plume burst, with a near-surface radius exceeding 1000 km, can develop from the hot lower-mantle material trapped in the second asthenosphere. Both the viscosity and the phase transition structure between 660 km and 1000 km can exert a significant influence on the plume distribution and cause singular plume eruption events in the upper mantle. Plume instabilities originating below the 660 km discontinuity in the western Pacific might have launched a large hot upwelling into the upper mantle, thus precipitating the massive flood basalt volcanism in the Ontong-Java region.

Modelling of helium transport in groundwater along a section in the Pannonian basin

Underground water flow in sedimentary basins controls the distribution of dissolved salts and gases, and their concentrations may therefore be used as indicators of the flow direction. Recent measurements of the 4He concentration in deep waters of the Pannonian basin have great importance in this respect. This paper presents an example of the simultaneous computation of water flow and helium distribution along a section crossing the Great Hungarian Plain. The model consists of three permeable layers. The boundaries of the layers are prescribed using geologic sections constrained by ample borehole and seismic data. The results of the finite-difference calculations are fitted to the observed helium concentrations using a least-squares algorithm that varies the model parameters. The significance of the model is that it reconstructs the structure and flux of the groundwater flow and estimates the poorly known hydrogeological parameters of the flow regime such as hydraulic conductivities, conductivity anisotropy and dispersion coefficients. The statistical uncertainty of the estimated parameters is around half an order of magnitude. An estimate of the regional average of the incoming helium flux is also obtained. The total helium flux in the Great Hungarian Plain at the surface is within the range observed in old stable continental areas of the Earth.