Bryan J. Travis

Convection in three dimensions with surface plates: Generation of toroidal flow

This work presents numerical calculations of mantle convection that incorporate some of the basic observational constraints imposed by plate tectonics. The model is three-dimensional and includes surface plates; it allows plate velocity to change dynamically according to the forces which result from convection. We show that plates are an effective means of introducing a toroidal component into the flow field. After initial transients the plate motion is nearly parallel to transform faults and in the direction that tends to minimizes the toroidal flow field. The toroidal field decays with depth from its value at the surface; the poloidal field is relatively constant throughout the layer but falls off slightly at the top and bottom boundaries. Layered viscosity increasing with depth causes the toroidal field to decay more rapidly, effectively confining it to the upper, low-viscosity layer. The effect of viscosity layering on the poloidal field is relatively small, which we attribute to its generation by temperature variations distributed throughout the system. The generation of toroidal flow by surface plates would seem to account for the observed nearly equal energy of toroidal and poloidal fields of plate motions on the Earth. A low-viscosity region in the upper mantle will cause the toroidal flow to decay significantly before reaching the lower mantle. The resulting concentration of toroidal flow in the upper mantle may result in more thorough mixing there and account for some of the geochemical and isotopic differences proposed to exist between the upper and lower mantles.

Biological reduction of uranium in groundwater and subsurface soil

Biological reduction of uranium is one of the techniques currently studied for in situ remediation of groundwater and subsurface soil. We investigated U(VI) reduction in groundwaters and soils of different origin to verify the presence of bacteria capable of U(VI) reduction. The groundwaters originated from mill tailings sites with U concentrations as high as 50 mg/l, and from other sites where uranium is not a contaminant, but was added in the laboratory to reach concentrations up to 11 mg/l. All waters contained nitrate and sulfate. After oxygen and nitrate reduction, U(VI) was reduced by sulfate-reducing bacteria, whose growth was stimulated by ethanol and trimetaphosphate. Uranium precipitated as hydrated uraninite (UO2 x xH2O). In the course of reduction of U(VI), Mn(IV) and Fe(III) from the soil were reduced as well. During uraninite precipitation a comparatively large mass of iron sulfides formed and served as a redox buffer. If the excess of iron sulfide is large enough, uraninite will not be oxidized by oxygenated groundwater. We show that bacteria capable of reducing U(VI) to U(IV) are ubiquitous in nature. The uranium reducers are primarily sulfate reducers and are stimulated by adding nutrients to the groundwater.

Lattice gas automata for flow through porous media

Abstract Lattice gas hydrodynamic models for flows through porous media in two and three dimensions are described. The computational method easily handles arbitrary boundaries and a large range of Reynolds numbers. Darcys law is confirmed for Poiseuille flow and for complicated boundary flows. Multiply connected pore structures similar to actual sandstone with fixed fractal dimension and porosity are generated. Permeability as a function of fractal dimension and porosity is calculated and compared with results of other methods and experiments.

Electromagnetic induction by a finite electric dipole source over a 2-D earth

A numerical solution for the frequency domain electromagnetic response of a two-dimensional (2-D) conductivity structure to excitation by a three-dimensional (3-D) current source has been developed. The fields are Fourier transformed in the invariant conductivity direction and then expressed in a variational form. At each of a set of discrete spatial wavenumbers a finite-element method is used to obtain a solution for the secondary electromagnetic fields. The finite element uses exponential elements to efficiently model the fields in the far-field. In combination with an iterative solution for the along-strike electromagnetic fields, this produces a considerable reduction in computation costs. The numerical solutions for a horizontal electric dipole are computed and shown to agree with closed form expressions and to converge with respect to the parameterization. Finally some simple examples of the electromagnetic fields produced by horizontal electric dipole sources at both the seafloor and air-earth interface are presented to illustrate the usefulness of the code.

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.

A benchmark comparison of numerical methods for infinite Prandtl number thermal convection in two-dimensional Cartesian geometry

Abstract A comparison is made between seven different numerical methods for calculating two-dimensional thermal convection in an infinite Prandtl number fluid. Among the seven methods are finite difference and finite element techniques that have been used to model thermal convection in the Earths mantle. We evaluate the performance of each method using a suite of four benchmark problems, ranging from steady-state convection to intrinsically time-dependent convection with recurring thermal boundary layer instabilities. These results can be used to determine the accuracy of other computational methods, and to assist in the development of new ones.

The transition from two-dimensional to three-dimensional planforms in infinite-Prandtl-number thermal convection

The stability of two-dimensional thermal convection in an infinite-Prandtl-number fluid layer with zero-stress boundaries is investigated using numerical calculations in three-dimensional rectangles. Time-dependent rolls are replaced by either bimodal or knot convection in cases where the horizontal dimensions of the rectangular box are less than twice the depth

Numerical modeling of chemically buoyant mantle plumes at spreading ridges

The geometry of spreading of plumes beneath midoceanic ridges is investigated by three-dimensional numerical modeling, with the goal of characterizing the width of the plume along the ridge, or the “waist width”. Chemically buoyant plumes are modeled, in order to compare to previously reported laboratory tank experiments. The plume is generated near the bottom of the box and rises and forms a mushroom-head with some entrainment of surrounding fluid. The head flattens at a considerable depth beneath the ridge before rising to the surface. Once the plume reaches the surface the head is quickly divided by the diverging plates, and the waist width is found to have reached a steady-state value, W. The results show that W is proportional to the square root of the volumetric flux of the plume divided by the diverging plate speed, which is consistent with previously reported experimental data. Our scaling law gives an independent method for estimating the volumetric flux of mantle plumes. The calculated plume fluxes are two to four times larger than previous estimates. If plume buoyancy is purely of thermal origin, then excess temperatures can be estimated from the fluxes. For Iceland, Azores and the Galapagos, the calculated excess temperatures are 140, 57, and 51°C respectively, in agreement with recent, independent estimates from modeling of gravity and bathymetry.

A lattice gas automata model for heterogeneous chemical reactions at mineral surfaces and in pore networks

Abstract A lattice gas automata (LGA) model is described which couples solute transport with chemical reactions at mineral surfaces and in pore networks. Chemical reactions and transport are integrated into a FHP-I LGA code as a module so that the approach is readily transportable to other codes. Diffusion in box calculations are compared to finite element Fickian diffusion results and provide an approach to quantifying space-time ratios of the models. Chemical reactions at solid surfaces, including precipitation/dissolution, sorption, and catalytic reaction, can be examined with the model because solute diffusion and mineral surface processes are all treated explicitly. The simplicity and flexibility of the LGA approach provides the ability to study the interrelationship between fluid flow and chemical reactions in porous materials, at a level of complexity that has not previously been computationally possible.

A model of high-frequency oscillatory potentials in retinal ganglion cells

High-frequency oscillatory potentials (HFOPs) have been recorded from ganglion cells in cat, rabbit, frog, and mudpuppy retina and in electroretinograms (ERGs) from humans and other primates. However, the origin of HFOPs is unknown. Based on patterns of tracer coupling, we hypothesized that HFOPs could be generated, in part, by negative feedback from axon-bearing amacrine cells excited via electrical synapses with neighboring ganglion cells. Computer simulations were used to determine whether such axon-mediated feedback was consistent with the experimentally observed properties of HFOPs. (1) Periodic signals are typically absent from ganglion cell PSTHs, in part because the phases of retinal HFOPs vary randomly over time and are only weakly stimulus locked. In the retinal model, this phase variability resulted from the nonlinear properties of axon-mediated feedback in combination with synaptic noise. (2) HFOPs increase as a function of stimulus size up to several times the receptive-field center diameter. In the model, axon-mediated feedback pooled signals over a large retinal area, producing HFOPs that were similarly size dependent. (3) HFOPs are stimulus specific. In the model, gap junctions between neighboring neurons caused contiguous regions to become phase locked, but did not synchronize separate regions. Model-generated HFOPs were consistent with the receptive-field center dynamics and spatial organization of cat alpha cells. HFOPs did not depend qualitatively on the exact value of any model parameter or on the numerical precision of the integration method. We conclude that HFOPs could be mediated, in part, by circuitry consistent with known retinal anatomy.