ALBERT

Notes: Previous work in nonequilibrium molecular dynamics (NEMD) has been restricted to systems subject only to pair interactions. We use methods of homogenous NEMD to investigate the nature of liquid sulfur under extreme shear using the potential model developed by Stillinger and Weber which involves explicitly three-body interaction. Simulations with up to 2048 particles have been carried out at a temperature of 1583 K and a density of 1.805 g cm−3 for shear rates between 0.005 and 1.75 in reduced units. We find that the fluid separates in sheets alternating from high to low density in planes perpendicular to the velocity gradient. No evidence is seen for the transition to the "string'' phase as exhibited by two-body systems. The molecules show a tendency to align in the direction of shear. Data are presented describing the magnitude of this effect.

Notes: Abstract Slab detachment is a geophysical instability whose manifestation can be revealed by seismic tomography. Evidence of this phenomenon is in the Dinarides/Hellenic and the New Hebrides subduction zones. Subducted slabs in these regions are torn horizontally at depths ranging from 100 to 300 km. We constructed a viscoelastic three-dimensional finite element model and investigated the state of stress. We found that an area with high stress concentration of the order of several hundred MPa is formed near the tip of the tear inside the slab, which can cause lateral migration of the tear. Favorable conditions for slab detachment are characterized by large interplate frictional force at a subduction zone and small slab resistance force deeper down. Stress concentration increases with the down-dip tension inside the slab. The phenomenon of slab weakening has also been studied from a thermal-mechanical standpoint, using a two-dimensional convection model with non-Newtonian, temperature-dependent rheology. The stress-dependent rheology plays an important role in causing local weakening of the descending slab. In strongly time-dependent situations the fast descending slab is not strong everywhere but has a weak region in the middle, making it vulnerable to slab detachment. The presence of viscous heating will enhance slab detachment tendency by further weakening the interior by the frictional heating. Besides these effects, there are other mechanisms which can also weaken the slab interior and help to make slabs more pliable and susceptible to detachment.

Notes: An initial-value theory is proposed for studying viscoelastic responses of compressible earth models with complex viscosity profiles. Continuous spectra are caused by both compressibility and the viscosity stratification, and they can cause numerical difficulties for the modal approach. We have studied the different responses for various types of viscosity profiles and found that there are differences in the responses at short wavelengths for viscosity profiles with sharp low-viscosity zones. We found that many modes are required to match the full initial-value solutions in the presence of sharp viscosity stratifications in both the upper and lower mantle. The normal-mode approach is best suited for simple layered models, long wavelengths and timescales greater than several thousand years, while the initial-value approach is indispensable in treating short-timescale problems with sharp low-viscosity zones in the upper mantle and viscosity stratification in the lower mantle.

Notes: We analyse the influences of a viscosity increase in the transition zone between 420 and 670 km on the geophysical signatures induced by post-glacial rebound, ranging from the perturbations in the Earth's rotation to the short wavelength features associated with the migration of the peripheral bulge. A self-gravitating model is adopted, consisting of an elastic lithosphere, a three-layer viscoelastic mantle and an inviscid core.The horizontal displacements and velocities and the stress pattern are extremely sensitive to the viscosity increase and to the chemical stratification of the transition zone. The hardening of the upper and the chemical density jumps in mantle below the 420 discontinuity induces a channel effect which contaminates the horizontal deformation both in the near-field and in the far-field from the ice-sheets. These findings indicate that intraplate geodetic data can be used to put bounds on the viscosity increase in the transition zone and on the amount of chemical stratification in the mantle.The stress field induced in the lithosphere by the Pleistocenic ice-sheet disintegration is a very sensitive function of mantle viscosity stratification. The existence of seismic activity along passive continental margins of previously glaciated areas requires a substantial viscosity increase in the mantle, with the viscosity of the transition zone acting as a controlling parameter. A viscously stratified mantle is responsible for a delayed upward migration of stress in the lithosphere which can account for the seismicity today.

Notes: A finite element method based on a primitive variables formulation is used to model both steady-state and time-dependent mantle convection with a composite Newtonian and non-Newtonian (power-law) rheology. The rheological model employs the transition stress as a means of partitioning the relative importance of the two rheologies. Results show that there is no direct correlation between viscosity and temperature anomalies. Fluctuations of the velocity fields are much greater and faster than for Newtonian flows. Fluctuations with amplitudes several times the background velocity are quite common. Intermittency effects with quiescent periods punctuated by chaotic bursts are observed. From scaling arguments temporal fluctuations of the volume-averaged viscosity are comparable in magnitude to the variations in the surface heat flow for the non-Newtonian flows, but are smaller than the variations in the velocity field. At larger transition stress the Newtonian behaviour becomes dominant and the temporal variations of the viscosity diminish. Both steady-state and time-dependent results show that for a given transition stress the non-Newtonian behaviour prevails to a greater extent with increasing Rayleigh number. Implications of this non-Newtonian tendency for Archaean tectonics are discussed.

Notes: Direct numerical simulations of two-dimensional high Rayleigh (Ra) number, base-heated thermal convection in large aspect-ratio boxes are presented for infinite Prandtl number fluids, as applied to the Earth's mantle. A transition is characterized in the flow structures in the neighborhood of Ra between 107 and 108. These high Ra flows consist of large-scale cells with strong intermittent, boundary-layer instabilities. For Ra exceeding 107 it is found that the heat-transfer mechanism changes from one characterized by mushroom-like plumes to one consisting of disconnected ascending instabilities, which do not carry with them all the thermal anomaly from the bottom boundary layer. Plume–plume collisions become much more prominent in high Ra situations and have a tendency of generating a pulse-like behavior in the fixed plume. This type of instability represents a distinct mode of heat transfer in the hard turbulent regime. Predictions of this model can be used to address certain issues concerning the mode of time-dependent convection in the Earth's mantle.

Notes: Recently there has developed a great deal of interest in the transition to hard turbulence in thermal convection. This transition and the corresponding hard turbulence regime has been the subject of laboratory and numerical experiments. Our study of convection at high Rayleigh numbers (Ra) has been motivated by the phenomenon of subsolidus mantle convection, whose Ra may range between 5×105 and O(108), depending on the still uncertain estimates of the lower-mantle viscosity. We have conducted a series of calculations at Ra spanning between 5×105 and 108 because we are interested in the transition from weak to strong turbulence in mantle convection and the effects this transition would have on mixing. We have employed a two-dimensional finite-element method, combined with an implicit, predictor–corrector, time-stepping scheme to advance the evolutionary temperature equation. The biharmonic equation for the streamfunction is solved exactly by a variational equation at each time step. We present direct numerical simulations of two-dimensional, high Ra thermal convection for constant property fluids with both base-heated and partially internally heated configurations in large-aspect-ratio boxes (up to 10).We will emphasize the importance of visualization of these strongly time-dependent results, as they present a formidable challenge in the management and analysis of the data. First, an adequate resolution of the boundary layer and mixing layer requires high resolution. In our large (10) aspect-ratio box runs we have employed around 27 000 unevenly spaced elements, resulting in about 105 unknowns per time step. Each run goes up to between 105 and 106 time steps in order to get many overturns of the dominant cells. We will present videos displaying the evolution of the physical fields, in particular the temperature and vorticity fields, which give a vivid portrayal of the mixing dynamics. Visualization is a handy medium for illustrating and also for discovering the richness of the mixing process, its multiple spatial and time scales in the transition from weak to strong turbulence. At Ra around 106, we have found that convection does not take place in a strictly cellular manner. Thermals emanate from the hot and cold boundary layers, which are superimposed on a large-scale type of circulation. These boundary layer instabilities enhance mixing of the interior.The fate of these instabilities is determined ultimately by the large-scale flow. With greater amounts of internal heating, the large-scale flow becomes smaller and mixing between distant regions is inhibited, but that between neighboring cells is enhanced by the changes of the flow pattern induced by internal heating. We have found a "mixing layer'' above the thermal boundary layer in the hard-turbulent regime. At high Ra, between 107 and 108, we find breakdown of globally connected thermal plumes for base-heated convection. In this hard-turbulent regime the plumes become disconnected, "podlike'' structures, thus inhibiting efficient vertical mixing. This disconnection of plumes in base-heated convection is to be regarded as a manifestation of the soft to hard turbulence transition. In the presence of internal heating and high Ra the descending cold boundary layers become dominant and serve to promote the interaction between the top and bottom, while the ascending plumes diminish in strength and disappear altogether. Mixing in the mantle thus influenced by the vigor in convection, the amount of internal heating, and the aspect ratio of the global configuration.

Notes: Time-dependent convection for infinite Prandtl number fluids has been investigated hitherto in the physical domain. Dynamics of plumelike structures resulting from boundary-layer instabilities can be interpreted in the spectral domain as having both direct and inverse cascades of energy taking place. In the physical domain only a small part of the spectrum is discernible. But the rest of the spectrum is needed for properly describing the nonlinear process. Only a relatively few modes, fewer than ten, are actually required for describing the essential features associated with the onset of plume dynamics.

Notes: [Auszug] Broad highlands16 in several geological areas, such as the Hoggar Massif, the East African plateaus and the northern Rocky Mountains surrounding Yellowstone, can be explained by a rapid increase in the lithospheric temperatures on a time scale of only 107 yr. Similar swells can also be found in ...