Numerical model of the supercontinental cycle stages: Integral transfer of the oceanic crust material and mantle viscous shear stresses

We compute the transfer of oceanic lithosphere material from the surface of the model to the inner convective mantle at successive stages of the supercontinental cycle, in the time interval from the beginning of convergence of the continents to their complete dispersal. The sequence of stages of a supercontinental cycle (Wilson cycle) is calculated with a two-dimensional numerical model of assembling and dispersing continents driven by mantle flows; in turn, the flows themselves are forming under thermal and mechanical influence of continents. We obtain that during the time of the order of 300 Myr the complete stirring of oceanic lithosphere through whole mantle does not occur. This agrees with current ideas on the circulation of oceanic crust material. Former oceanic crust material appears again at the Earth’s surface in the areas of mantle upstreams. The numerical simulation demonstrates that the supercontinental cycle is a factor which intensifies stirring of the material, especially in the region beneath the supercontinent. The reasons are a recurring formation of plumes in that region as well as a global restructuring of mantle flow pattern due to the process of joining and separation of continents. The computations of viscous shear stresses are also carried out in the mantle as a function of spatial coordinates and time. With a simplified model of uniform mantle viscosity, the numerical experiment shows that the typical maximal shear stresses in the major portion of the mantle measure about 5 MPa (50 bar). The typical maximal shear stresses located in the uppermost part of mantle downgoing streams (in a zone that measures roughly 200 × 200 km) are approximately 8 times greater and equal to 40 MPa (400 bar).     

Progress in the numerical modeling of mantle plumes

The mantle plume model, as an integral part of the Earth’s internal convection system, is complementary to the theory of plate tectonics. They together constitute the key configuration of material circulation and energy transport in the Earth’s interior. Seismology, high-temperature and high-pressure mineralogy, geology, and geodynamic numerical modeling have conducted comprehensive studies on the mantle plume model since it was proposed. In particular, numerical simulation, which investigates t...     

Horizontal stresses in the mantle and in the moving continent for the model of two-dimensional convection with varying viscosity

Numerical experiments on studying the spatial fields and evolution of viscous overlithostatic horizontal stresses and pressure in the mantle and in the moving continent are carried out. The continent moves consistently with time-dependent forces, which act from the viscous mantle. By introducing the varying viscosity, we gain the possibility for taking into account the oceanic lithosphere and the difference between the viscosity of the upper and the lower mantle in the context of a purely viscous model. The typical overlithostatic horizontal stresses in the main part of the mantle are ±(7–9) MPa (70–90 bar); in the highly viscous regions and, particularly, in the subduction zones they are at least three times larger. The descending mantle flows in the depth interval from approximately 50 km to about 300 km are more sharply pronounced in the pressure field than in the field of horizontal stresses. At the considered stages of motion and in different parts, the continent is characterized by the following typical values of stresses: the overlithostatic pressure ranges from ?5 to +15 MPa; the horizontal overlithostatic tensile stress amounts up to ?4MPa (?40 bar); and the compressive stress in case of the overriding of the subduction zone attains +35 MPa (350 bar).     

Parameterized thermal model of a mixed mantle convection

IntroductionTectonicevolutionisinfluencedbythermalhistoryoftheEarth.TheEarthhasabout4.6Gahistory.ThermalenergyfromtheinterioroftheEachprovidesthemainpowerfortectonicevolution.ItnotonlycontrolstheformationofthelayeredstructuresinsidetheEarth,butalsopromotesthetectonicmovementsofthesurfaceplatesduringthegeologicalera.ThestudyofthethermalhistoryoftheEarthhaspassedseveralstages.Inearlystudies,onlyconductivemechanism(Lubimova,1958)isdiscussedinthethermalevolution.However,theimpotalceofthermalco…     

On the stresses produced in a liquid-saturated porous solid by normal and tangential forces on a moving strip of finite width

Summary This paper deals with the stresses produced in a semi-infinite liquid-saturated porous solid of the type considered byBiot [1]²), by moving normal and tangential forces acting simultaneously on a moving strip of finite width on the free surface. It has been found that the stresses can be obtained in a closed form. It has also been found that if the velocity of the strip exceeds a certain value, the nature of the stresses changes, and there are discontinuities of stress along certain lines. The results have been applied to study the changes in the stresses produced by moving normal and tangential forces with depth and distance.     

上地幔俯冲板块的动力学过程:数值模拟

大洋板块俯冲到地幔转换带,进而可形成不同的形态：板块可以停滞在660 km不连续面,抑或穿过地幔转换带进入下地幔.这些不同的俯冲模式可进一步影响到海沟的运动.为更好地理解上地幔中俯冲板片的变形行为以及俯冲过程与海沟运动之间的关系,本文通过建立一系列高精度二维热-力学自由俯冲的数值模型,揭示了俯冲板块在上地幔中的变形方式及其与地幔转换带之间的相互作用过程.模拟结果显示,在俯冲板块与地幔转换带的相互作用过程中,其动力学过程可以分为以海沟后撤主导、海沟前进主导以及稳定型海沟等三种主要动力学类型.对于年龄较老,厚度较大的俯冲板块容易形成海沟后撤型俯冲,俯冲板块停滞在660 km不连续面.相反,年龄较小,塑性强度较小的板块容易形成海沟前进型俯冲,俯冲板块穿越660 km不连续面.

     

Three-dimensional numerical simulations of crustal deformation and subcontinental mantle convection

3-D simulations of mantle convection allowing for continental crust are explored to study the effects of crustal thickening on lithosphere stability and of continents on large-scale mantle flow. Simulations begin with a crustal layer within the upper thermal boundary layer of a mantle convection roll in a 1 × 1 × 1 Cartesian domain. Convective stresses cause crust to thicken above a sheet-like mantle downwelling. For mild convective vigor an initial crustal thickness variation is required to induce 3-D lithospheric instability below the zone of crustal convergence. The amplitude of the required variation decreases with increasing convective vigor. Morphologically, instability is manifest in formation of drip-like thermals that exist within the large-scale roll associated with initial crustal thickening. A strong surface signature of the drips is their ability to cause deviations from local Airy compensation of topography. After the initial thickening phase, the crustal accumulation that forms serves as a model analog to a continent. Its presence leads to mantle flow patterns distinctly different from the steady-state roll that results in its absence. Large lateral thermal gradients are generated at its edge allowing this region to be the initiation site for continued small-scale thermal instabilities. Eventually these instabilities induce a restructuring of large-scale mantle flow, with the roll pattern being replaced by a square cell. Although preliminary and idealized, the simulations do show the fluid dynamical plausibility behind the idea that significant mantle variations can be generated along the strike of a largely 2-D mountain chain by the formation of the chain itself. The ability of a model continent to cause a change in fundamental convective planform also suggests that the effects of continental crust on mantle convection may be low-order despite the seemingly trivial volume of crust relative to mantle.     

The effect of sloped isotherms on melt migration in the shallow mantle: a physical and numerical model based on observations in the Oman ophiolite

Field observations in the Oman ophiolite and petrological data are used to constrain a model of melt segregation at the top of the mantle beneath an oceanic spreading centre. Foliations and lineations in outcrops of mantle-derived peridotites oriented at high angle relative to the crust–mantle boundary have been interpreted as the footprint of a former axial asthenospheric convective upwelling several kilometers in cross-section that reached Moho levels. Basaltic melts migrating through this upwelling reacted with their host harzburgites and suffered fractional crystallization. The mantle–crust transition zone at the top of the upwelling is characterized by an very thick (about 400 m) dunite layer whose detailed structure and composition point to the development by compaction of a former “mantle mush”. The more important structures (in terms of volume of crystallization products) found in the underlying harzburgites are dunitic–troctolitic horizons a few meters thick and of lateral extent reaching 1 km and more. They crystallized at high temperature (>1190 °C) from melts similar to mid-ocean ridge basalts (MORB). These are called “sills” because they are sub-parallel to the crust–mantle boundary, but they can present a moderate dip (15° to 20° at most) relative to this paleo-horizontal surface. These observations have motivated the modelling of melt segregation by compaction within the crystallization domain inside the top convective boundary layer of the mantle upwelling. Two original inputs to the modelling are considered here: (i) the slope of the iso-curves of melt concentration due to the progressive cooling of the mantle in the boundary layer away from the axis of the rising convective flow; (ii) the reduction in permeability caused by the crystallization of the inter-granular melt. Modelling shows that a unique condition is required to generate the troctolite sills and the thick dunite layer nested at the top of the Maqsad diapir: namely a dramatic drop of the interstitial melt concentration at the top of the mantle. Besides, the model developed here allows to scale the time, volume and velocity of the melt segregation.     

Upper mantle convection driving by density anomaly and a test model

Introduction Richter and Mckenzie (1978) supposed that there is a small-scale convection system in the mantle. For a long time lots of research provides observational data to infer the possibility of a small-scale convection in the upper mantle. For example, Haxby and Weissel (1986) discussed the relationship between SEASAT map and small-scale convection. Baudry and Kroenke (1991), Maia and Diament (1991) found that the geoid and bathymetry exhibit peaks in the 400~650 km range in the Pa…     

Assessing a numerical cellular braided‐stream model with a physical model

A. B. Murray and C. Paola (1994, Nature, vol. 371, pp. 54–57; 1997, Earth Surface Processes and Landforms, vol. 22, pp. 1001–1025) proposed a cellular model for braided river dynamics as an exploratory device for investigating the conditions necessary for the occurrence of braiding. The model reproduces a number of the general morphological and dynamic features of braided rivers in a simplified form. Here we test the representation of braided channel morphodynamics in the Murray–Paola model against the known characteristics (mainly from a sequence of high resolution digital elevation models) of a physical model of a braided stream. The overall aim is to further the goals of the exploratory modelling approach by first investigating the capabilities and limitations of the existing model and then by proposing modifications and alternative approaches to modelling of the essential features of braiding. The model confirms the general inferences of Murray and Paola (1997) about model performance. However, the modelled evolution shows little resemblance to the real evolution of the small‐scale laboratory river, although this depends to some extent on the coarseness of the grid used in the model relative to the scale of the topography. The model does not reproduce the bar‐scale topography and dynamics even when the grid scale and amplitude of topography are adapted to be equivalent to the original Murray–Paola results. Strong dependence of the modelled processes on local bed slopes and the tendency for the model to adopt its own intrinsic scale, rather than adapt to the scale of the pre‐existing topography, appear to be the main causes of the differences between numerical model results and the physical model morphology and dynamics. The model performance can be improved by modification of the model equations to more closely represent the water surface but as an exploratory approach hierarchical modelling promises greater success in overcoming the identified shortcomings. Copyright © 2005 John Wiley & Sons, Ltd.     

Calibration of a numerical ionospheric model with EISCAT observations

A set of EISCAT UHF and VHP observations is used for calibrating a coupled fluid-kinetic model of the ionosphere. The data gathered in the period 1200–2400 UT on 24 March 1995 had various intervals of interest for such a calibration. The magnetospheric activity was very low during the afternoon, allowing for a proper examination of a case of quiet ionospheric conditions. The radars entered the auroral oval just after 1900 UT: a series of dynamic events probably associated with rapidly moving auroral arcs was observed until after 2200 UT. No attempts were made to model the dynamical behaviour during the 1900–2200 UT period. In contrast, the period 2200–2400 UT was characterised by quite steady precipitation: this latter period was then chosen for calibrating the model during precipitation events. The adjustment of the model on the four primary parameters observed by the radars (namely the electron concentration and temperature and the ion temperature and velocity) needed external inputs (solar fluxes and magnetic activity index) and the adjustments of a neutral atmospheric model in order to reach a good agreement. It is shown that for the quiet ionosphere, only slight adjustments of the neutral atmosphere models are needed. In contrast, adjusting the observations during the precipitation event requires strong departures from the model, both for the atomic oxygen and hydrogen. However, it is argued that this could well be the result of inadequately representing the vibrational states of N₂ during precipitation events, and that these factors have to be considered only as ad hoc corrections.     

地幔热导率的选取对动力学数值模拟的影响——以岩石圈张裂过程为例

目前存在有多种地幔热导率模型,不同模型在数值和随温压变化的特征上有明显的差异.为探究不同热导率模型对动力学数值模拟结果的影响,本文对不同模型下的岩石圈张裂过程进行模拟研究,探讨地幔热导率对岩石圈热传输、变形和熔融过程的影响及其作用机理.结果显示,不同热导率模型下,岩石圈的变形和熔融特征表现出明显差异.高热导率模型下,岩石圈破裂较晚,形成陆缘较为宽阔,地壳熔融强烈而地幔熔融较弱;低热导率模型下,岩石圈破裂较早,形成陆缘较为狭窄,地幔熔融强烈而地壳熔融较弱.这种差异源于不同地幔热导率下岩石圈和地幔热状态的变化及相应力学性质的改变.高热导率下,热传导的增温效应显著,岩石圈呈现较热的状态,其强度整体较低,壳幔耦合减弱;而低热导率下,热对流的增温效应显著,岩石圈呈较冷的状态,其强度整体较高,壳幔耦合增强.基于模拟结果,本文认为地幔热导率的选取对动力学模拟的结果有着较为显著的影响,相对于随温压的变化,热导率数值的差异对动力学数值模拟的结果影响更大,尤其是对于地幔熔融过程的影响.

     

A quasi-geostrophic numerical model of a rotating internally heated fluid

Abstract

A quasi-geostrophic numerical model of flow in a rotating channel is integrated under conditions typical of laboratory experiments with an internally heated annulus system. Compared to a laboratory experiment, or a full Navier-Stokes simulation, the quasi geostrophic numerical model is a simple system. It includes nonlinear interactions, dissipation via conventional parameterizations of Ekman layers and internal diffusion, and a steady forcing term which represents heating near the centre of the channel and cooling near both sides. Explicit boundary layers, cylindrical geometry effects, horizontal variations in static stability and variations in conductivity and diffusivity with temperature are all absent, and ageostrophic advection is incompletely represented. Nevertheless, over a range of parameters, flows are produced which strongly resemble those seen in the laboratory thus suggesting that the most important physical processes are represented. The numerical model is used to map out a regime diagram which includes examples of steady flows, flows with periodic time dependence (wavenumber vacillations) and flows which are irregularly time dependent.     

Mechanisms of bottom boundary fluxes in a numerical model of the Shetland shelf

Across-slope bottom boundary layer (BBL) fluxes on the shelf-edge connect this region to deeper waters. Two proposed ways in which across-slope BBL fluxes can occur, in regions that have a slope current aligned to the bathymetry, are the frictional veering of bottom currents termed the ‘Ekman drain’ and through local wind-forced downwelling (wind-driven surface Ekman flow with an associated bottom flow). We investigate the variability, magnitude and spatial scale of BBL fluxes on the Shetland shelf, which has a prominent slope current, using a high-resolution (～2 km) configuration of the MITgcm model. Fluxes are analysed in the BBL at the shelf break near the 200 m isobath and are found to have a seasonal variability with high/low volume transport in winter/summer respectively. By using a multivariate regression approach, we find that the locally wind-driven Ekman transport plays no explicit role in explaining daily bottom fluxes. We can better explain the variability of the across-slope BBL flux as a linear function of the speed and across-slope component of the interior flow, corresponding to an Ekman plus mean-flow flux. We estimate that the mean-flow is a greater contributor than the Ekman flux to the BBL flux. The spatial heterogeneity of the BBL fluxes can be attributed to the mean-flow, which has a much shorter decorrelation length compared to the Ekman flux. We conclude that both the speed and direction of the interior current determines the daily BBL flux. The wind does not explicitly contribute through local downwelling, but may influence the interior current and therefore implicitly the BBL fluxes on longer timescales.     

Hot-spots,mantle plumes and a model for the origin of ultramafic xenoliths in alkali basalts

The Wilson-Morgan hypothesis of hot-spots, characterized by high heat flow, positive gravity anomaly and alkalic volcanism, assumes that such hot-spots are surface expressions of mantle plumes rising by thermal convection. Possible evidence of this mantle upwelling is shown here from textural, structural and chemical aspects of ultramafic xenoliths in alkalic basalts. The xenolith-bearing basalts are constanly associated with Wilson-Morgan hot-spots in the ocean basins and with their continental counterparts in the rift valleys which show extensional tectonics. Most of the xenoliths are considered to be accidental fragments of the lithosphere in the host basalts. One remarkable aspect of xenoliths from all parts of the world is their ubiquitous tectonite fabric. The microstructures of these xenoliths are due to plastic deformation. Some of the xenoliths from Baja California show characteristic deformational features which are also found in the marginal parts of diapirically intruded high-temperature peridotite massifs. A model is proposed for the origin of xenoliths in alkalic basalts by mantle upwelling in which the plastic deformation of the xenoliths reflects this dynamic uprise.     

Parameterization of a spherically symmetrical earth model with special references to the upper mantle

The advantages of using relatively simple polynomial parameterizations of the velocities and density within the earth in inversions of the free oscillation and travel time data set are discussed with special reference to the development of a standard earth model.     

Turbulent mixing in the Northern North Sea: a numerical model study

The aim of this study is to intervalidate observations and numerical simulation results for the turbulent dissipation rate under strong wind conditions in the Northern North Sea during one week in October 1998. The observations were obtained by spatially and temporally averaging measurements of small-scale shear with a free-falling shear probe. The 1D numerical model used for this study is based on a state-of-the-art two-equation k− turbulence model with an algebraic second-moment closure scheme. It is discussed by means of annual and seasonal model simulations how the influence of heat and salt advection and internal waves can be accounted for. After these precautions, the agreement between observations and simulations of the turbulent dissipation rate are fairly good. Remaining differences cannot only be explained by problems such as undersampling and noise level, but also by idealising model assumptions.     

Magnetic clouds and interplanetary particle transport: a numerical model

Magnetic clouds modify the structure of the interplanetary magnetic field on spatial scales of tenth of AU. Their influence on the transport of energetic charged particles is studied with a numerical model that treats the magnetic cloud as an outward propagating modification of the focusing length. As a rule of thumb, the influence of the magnetic cloud on particle intensity and anisotropy profiles increases with decreasing particle mean free path and decreasing particle speed. Three cases are considered: (1) when the magnetic cloud is the driver of a shock that accelerates particles as it propagates outward, (2) when the magnetic cloud interacts with a prior solar energetic particle event, and (3) when a magnetic cloud already is present in interplanetary space at the time of a solar energetic particle event. In the latter case the cloud acts as a barrier, storing the bulk of the particles in its downstream medium.     

A numerical oil spill model based on a hybrid method

The purpose of this paper is the development of a hybrid particle tracking/Eulerian-Lagrangian approach for the simulation of spilled oil in coastal areas. Oil discharge from the source is modeled by the release of particles. When the oil slick thickness or the oil concentration reaches a critical value, particles are mapped on slick thickness or node concentrations, and the calculations proceed in the Eulerian-Lagrangian mode. To acquire accurate environment information, the model is coupled with the 3-D free-surface hydrodynamics model (POM) and the third-generation wave model (SWAN). By simulating the oil processes of spreading, advection, turbulent diffusion, evaporation, emulsification, dissolution and shoreline deposition, it has the ability to predict the horizontal movement of surface oil slick, the vertical distribution of oil particles, the concentration in the water column and the mass balance of spilled oil. An accidental oil release near Dalian coastal waters is simulated to validate the developed model. Compared with the satellite images of oil slicks on the surface, the numerical results indicate that the model has a reasonable accuracy.     

Carbon cycle and climate change during the Cretaceous inferred from a biogeochemical carbon cycle model

The carbon cycle and climate change during the Cretaceous are reconstructed by using a carbon cycle model, and discussed. The model takes into account the effects of the enhanced magma eruption and organic carbon burial rates, both of which characterize the carbon cycle during the Cretaceous. The result for the CO₂ variation is roughly consistent with the pattern of paleoclimate change inferred from the geological record. The CO₂ level during the mid-Cretaceous is estimated to be 4–5 times the present atmospheric level, corresponding to a surface temperature of 20–21°C. The warm, equable Cretaceous resulted from the effects of tectonic forcing such as enhanced CO₂ degassing, although the enhanced organic carbon burial has a tendency to decrease the CO₂ level. The organic carbon burial rate during the Cretaceous is generally larger than those for the Cenozoic, and is characterized by three major peaks (~ 1.5–1.8 times the present-day value) corresponding to the major oceanic anoxic events. In the case for the extensive mantle plume degassing, although the CO₂ levels are only 10% higher than those for the standard case during 120–100 Ma, the causes for the enhanced CO₂ levels would be quite different. If the globally averaged surface temperature had increased due to paleogeographic forcing effects, the greenhouse effect of CO₂ (and thus the CO₂ level) should be lower than the values estimated for the standard case. If the CO₂ levels are similar to, but the surface temperature is higher than, those for the standard case, either the parameter β (an influence of the Himalayas–Tibetan Plateau on the global weathering today) may be unreasonably large or the dependence of the silicate weathering rate on the CO₂ partial pressure and the surface temperature should be much weaker than those previously proposed.