Models of plate tectonics with the Lattice Boltzmann Method
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Mora, Peter (ORCID:000000015347446X)↗
Engineering topics
Yuen, David A.
Publications and source records attributed to Yuen, David A..
Volumetric Rendering on Wavelet-Based Adaptive Grid
Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.
Vezolainen, Alexei V.↗
Dynamical consequences on fast subducting slabs from a self-regulating mechanism due to viscous heating in variable viscosity convection
We have studied 2-D time-dependent convection for a rheology which is both non-Newtonian and temperature-dependent. Strong effects associated with viscous heating are found in the downwelling sheets, which are heated on both sides with an intensity around O(100) times the chondritic value. The magnitude of viscous heating increases strongly with the subduction speed. The slab interior is weakened by viscous heating and slab breakoff then takes place. This process provides a self-regulating mechanism for governing the speed of intact slabs able to reach the deep mantle. Timescales associated with viscous heating are quite short, a few million years. Internal heating by radioactivity decreases the amount of shear heating.
Larsen, Tine B.↗
Rheological transition in mantle convection with a composite temperature-dependent, non-Newtonian and Newtonian rheology
Numerical simulations of mantle convection with a composite temperature-dependent, Newtonian and non-Newtonian creep law have revealed a transition in the dominant creep mechanism with the increasing vigour of convection. Newtonian creep is found to dominate in the low Rayleigh number regime. With sufficiently high effective Rayleigh number, the overall creep mechanism in the convective flow becomes non-Newtonian. The transitional Rayleigh number increases strongly with the activation energy. These results would suggest a scenario that in the early epochs of Earth the flow in the mantle would have been governed by non-Newtonian rheology and would have exhibited both strong spatial and temporal fluctuations. With time the flow mechanism would behave like a Newtonian fluid and would have a different time-dependent character. In time-dependent Newtonian-dominated flows there are still localized features with distinctly non-Newtonian character. Our analysis of the relative contributions to the lateral viscosity field supports the idea that the inference of the nature of lateral viscosity heterogeneities by seismic tomography may be strongly contaminated by the dominant non-Newtonian contributions to the total lateral viscosity field.
Van Den Berg, Arie P.↗
Dynamical influences on the moment of inertia tensor from lateral viscosity variations inferred from seismic tomographic models
We have investigated the influences of lateral variations of viscosity on the moment of inertia tensor from viscous flows due to the density anomalies in the mantle inferred from seismic tomographic models. The scaling relations between the density and the seismic anomalies is taken as either a constant or a function increasing with depth in accord with the recent high-pressure experimental studies. The viscosity is taken as an exponential function of the 3D density anomaly. In models with an isoviscous background, the effects on the perturbed moment of inertia tensor from the lateral viscosity variations are smaller than those due to variations in the radial viscosity profiles. In mantle models with a background viscosity increasing with depth, the influences of the lateral viscosity variations are significant. The most striking feature in the latter case is that the two off-diagonal elements delta I(sub xz) and delta I(sub yz) in the inertia tensor exhibit greatest sensitivity to lateral variations of the viscosity. While the other elements of the inertia change by only about a few tens of percent in the range of lateral viscosity contrast considered (less than 300), delta I(sub xz) and delta I(sub yz) can vary up to 40 times even with a change in sign, depending on the radial viscosity stratification and the location of the strongest lateral variations. The increase in the velocity-density scaling relation with depth can reduce the influences of the lateral viscosity variations, but it does not change the overall sensitive nature of delta I(sub xz) and delta I(sub yz). This study demonstrates clearly that the lateral viscosity variations, especially in the upper mantle, must be considered in the determination of long-term polar wander, since the variations in the delta I(sub xz) and delta I(sub yz) terms are directly responsible for exciting rotational movements.
Zhang, Shuxia↗
Reply to the comment by Y. Ricard, R. Sabadini, and G. Spada
We welcome this opportunity which Drs. Ricard, Sabadini and Spada (RSS) have offered us to elaborate on some points concerning the connection between convective circulations and rotational dynamics. The relationship of the linear viscoelastic normal-mode theory to other approaches, such as viscous and the non-linear viscoelastic treatments, can be found in Moser et al. (1993). We will address the issues raised by RSS by first going over the reference system. This will be followed by a discussion concerning long-term polar wander and relative angular momentum. We will also go over the issues concerning the off-diagonal terms in the total moment of inertia and polar wander.
Moser, Jiri↗
Polar motions excited by a convecting viscous mantle
The role played by time-dependent mantle convection on exciting long-term polar motions is examined by means of a viscous model. For sufficiently low effective viscosity, polar-wander speeds of 0(1 deg/Myr) would require contributions from the off-diagonal elements of the inertia tensor, with magnitudes around 100,000 times smaller than those found in viscoelastic models used for postglacial rebound. Contributions from the large-scale mantle flow to the angular momentum vector can be comparable to those due to changes in moment of inertia tensor for nonlinear rheology or for young planet. The relative roles of the two contributions depend on the nonlinear rheology of the mantle and its convective vigor.
Moser, Jiri↗
Postglacial rebound with a non-Newtonian upper mantle and a Newtonian lower mantle rheology
A composite rheology is employed consisting of both linear and nonlinear creep mechanisms which are connected by a 'transition' stress. Background stress due to geodynamical processes is included. For models with a non-Newtonian upper-mantle overlying a Newtonian lower-mantle, the temporal responses of the displacements can reproduce those of Newtonian models. The average effective viscosity profile under the ice-load at the end of deglaciation turns out to be the crucial factor governing mantle relaxation. This can explain why simple Newtonian rheology has been successful in fitting the uplift data over formerly glaciated regions.
Gasperini, Paolo↗
Effects on post-glacial rebound from the hard rheology in the transition zone
The effect of an increase of viscosity in the earth-mantle's transition zone between 420 and 670 km on the geophysical signatures induced by postglacial rebound was analyzed using a self-gravitating model consisting of an elastic lithosphere, a three-layer viscoelastic mantle, and an inviscid core. Results show that the horizontal displacements and velocities as well as the stress pattern are extremely sensitive to the viscosity increase and to the chemical stratification of the transition zone. The findings indicate that geodetic data on intraplate deformation can be used to put constraints on the viscosity increase in the transition zone and on the amount of chemical stratification in the mantle.
Spada, Giorgio↗
The role of hard turbulent thermal convection in the Earth's early thermal evolution
In the last several years great progress was made in the study of a new transition in thermal convection, called hard turbulence. Initial experiments were conducted with helium gas, then with water. It was shown that for base-heated Newtonian convection a transition occurred at Rayleigh numbers between 10(exp 7) and 10(exp 8). This transition is characterized by the appearance of disconnected plume structures in contrast to continuous plumes with mushroom-shaped tops found for lower Rayleigh numbers. This new hydrodynamic transition is expected to play an important role in reshaping our concepts of mantle convection in the early stages of planetary evolution. We have conducted two-dimensional calculations for large and small aspect-ratio configuration to see whether such a transition would take place for infinite Prandtl number fluids.
Hansen, Ulli↗
Effects of depth-variations in creep laws on the formation of plates in mantle dynamics
The influences of depth-varying rheologies on the structure of mantle convection and the near surface flow fields are studied. Upwelling flows crossing the upper-lower mantle boundary become considerably thinner and faster. Streamlines are concentrated near the surface and other platelike characteristics are enhanced by this type of rheological stratification in which the averaged effective viscosity of the upper mantle is about two orders of magnitude lower than that of the lower mantle. The presence of a lithosphere with a higher nonlinear dependence in the flow law further promotes platelike behavior. Platelike character of the top boundary-layer is encouraged by a decreasing depth-dependent viscosity in the non-Newtonian upper-mantle and by greater convective vigor.
Van Den Berg, Arie P.↗
Viscoelastic responses of a hard transition zone - Effects on postglacial uplifts and rotational signatures
A five-layer viscoelastic spherical model is used to calculate the transient displacements of postglacial rebound, the induced polar motions, and the temporal variations of the geopotential up to degree 8 of the zonal coefficients. Two models - one with two viscoelastic layers separated at 670 km, and the other with three layers in which a hard garnet layer lies between the upper and lower mantle - are compared. Forward modeling shows that it may be possible to discern the presence of a hard garnet layer with a viscosity of at least ten times greater than the upper mantle, on the basis of uplift data near the center of the former Laurentide ice-sheet and from polar wander and j2 data. Temporal variations of higher gravity harmonics, such as j6 and j8, can potentially place even tighter constraints on the rheological properties of the hard transition zone. A lower mantle viscosity between 2 and 4 x 10 to the 22nd Pa is generally preferred in models with a garnet layer which may be as large as 50 times more viscous than the upper mantle.
Spada, Giorgio↗
Effects of depth-dependent thermal expansivity on mantle circulations and lateral thermal anomalies
The influences of depth-dependent thermal expansivity on the structure of Newtonian thermal convection and lateral thermal anomalies are studied. In an aspect-ratio ten box the effects of the depth-dependent expansivity are to produce large aspect-ratio cells with a few relatively stationary upwellings. The lateral thermal anomalies in the lower mantle are greatly diminished by depth-dependent expansivity. This together with a decrease in the temperature derivative of seismic velocities in the lower mantle would support the low level of lateral heterogeneities found in recent tomographic studies.
Hansen, Ulrich↗
Transition to hard turbulence in thermal convection at infinite Prandtl number
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 characaterized in the flow structures in the neighborhood of Ra between 10 to the 7th and 10 to the 8th. These high Ra flows consist of large-scale cells with strong intermittent, boundary-layer instabilities. For Ra exceeding 10 to the 7th 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.
Hansen, Ulrich↗
Dynamical effects from equation of state on topographies and geoid anomalies due to internal loading
Using a Cartesian compressible model, the effects of compressibility on geoid anomalies and of deformations on the topographic signatures caused by internal loading in the mantle are quantitatively investigated by examining different types of the equation of state. Also considered are different types of density laws with variations of thermodynamical parameters taken into play. It is shown that surface topographies are not changed much by the effects of mantle compressibility and that the deformation of bottom boundary is not significantly influenced except for long wavelengths and large viscosity contrasts between the upper and lower mantles. On the other hand, mantle compressibility can greatly affect geoid signals with horizontal wavelengths exceeding 10,000 km.
Hong, Hanjing↗
Molecular dynamics of liquid SiO2 under high pressure
The molecular dynamics of pure SiO2 liquids was investigated up to pressures of 20 GPa at 4000 K using 252, 498, 864, and 1371 particles. The results obtained suggest that the pressure-induced maxima in the self-diffusion coefficients of both oxygen and silicon are dependent on the system size. In the case of larger systems, the maximum decreases and shifts to lower pressures. Changes in the velocity autocorrelation function with increasing pressure are described. The populations of anomalously coordinated silicon and oxygen are then discussed as a function of pressure and system size.
Rustad, James R.↗