Engineering topics

Yuen, D. A.

Publications and source records attributed to Yuen, D. A..

At least 19 records

NASA NTRS1995

Time-domain approach for the transient responses in stratified viscoelastic Earth models

We have developed the numerical algorithm for the computation of transient viscoelastic responses in the time domain for a radially stratified Earth model. Stratifications in both the elastic parameters and the viscosity profile have been considered. The particular viscosity profile employed has a viscosity maximum with a constrast of O(100) in the mid lower mantle. The distribution of relaxation times reveals the presence of a continuous spectrum situated between O(100) and O(exp 4) years. The principal mode is embedded within this continuous spectrum. From this initial-value approach we have found that for the low degree harmonics the non-modal contributions are comparable to the modal contributions. For this viscosity model the differences between the time-domain and normal-mode results are found to decrease strongly with increasing angular order. These calculations also show that a time-dependent effective relaxation time can be defined, which can be bounded by the relaxation times of the principal modes.

Hanyk, L.↗

NASA NTRS1995

Localization of toroidal motion and shear heating in 3-D high Rayleigh number convection with temperature-dependent viscosity

We have applied spectral-transform methods to study three-dimensional thermal convection with temperature-dependent viscosity. The viscosity varies exponentially with the form exp(-BT), where B controls the viscosity contrast and T is temperature. Solutions for high Rayleigh numbers, up to an effective Ra of 6.25 x 10(exp 6), have been obtained for an aspect-ratio of 5x5x1 and a viscosity contrast of 25. Solutions show the localization of toroidal velocity fields with increasing vigor of convection to a coherent network of shear-zones. Viscous dissipation increases with Rayleigh number and is particularly strong in regions of convergent flows and shear deformation. A time-varying depth-dependent mean-flow is generated because of the correlation between laterally varying viscosity and velocity gradients.

Balachandar, S.↗

NASA NTRS1994

Three-dimensional fully spectral numerical method for mantle convection with depth-dependent properties

A semi-implicit fully spectral collocation method for the simulation of three-dimensional mantle convection with depth-dependent thermo-dynamic and transport properties is presented. The variable property Navier-Stokes equation expressed in terms of the primitive variable velocity and pressure is solved with the mass continuity and temperature equations. The periodic horizontal boundary conditions allow a Fourier expansion for the two horizontal directions. The stress-free, impermeable isothermal boundary conditions along with the depth dependent coefficients are handled with a Chebyshev expansion in the vertical direction. In the limit of an infinite Prandtl number appropriate to mantle convection, the inertial terms in the momentum equation are unimportant. In this case an explicit solution of a Poisson equation for pressure can be avoided; instead a fourth-order equation for vertical velocity can be solved. Simultaneous imposition of both impermeable and continuity boundary conditions during the vertical velocity evaluation is discussed. The pressure distributions on the top and bottom bounding planes were determined by means of an influence matrix technique. The numerical method employed here avoids time-splitting errors and enforces velocity boundary conditions and continuity over the entire domain, including the boundaries, to machine accuracy. Strongly time-dependent three-dimensional solutions up to a surface Rayleigh number of 1 x 10(exp 7) have been obtained. Strong upwellings, pulsating chaotically, are formed by the collective merging of cylindrical plumes.

Balachandar, S.↗

NASA NTRS1994

Lower mantle thermal structure deduced from seismic tomography, mineral physics and numerical modelling

The long-wavelength thermal anomalies in the lower mantle have been mapped out using several seismic tomographic models in conjunction with thermodynamic parameters derived from high-pressure mineral physics experiments. These parameters are the depth variations of thermal expansivity and of the proportionality factor between changes in density and seismic velocity. The giant plume-like structures in the lower mantle under the Pacific Ocean and Africa have outer fringes with thermal anomalies around 300-400 K, but very high temperatures are found in the center of the plumes near the base of the core-mantle boundary. These extreme values can exceed +1500 K and may reflect large hot thermal anomalies in the lower mantle, which are supported by recent measurements of high melting temperatures of perovskite and iron. Extremely cold anomalies, around -1500 K, are found for anomalies in the deep mantle around the Pacific rim and under South America. Numerical simulations show that large negative thermal anomalies in the mid-lower mantle have modest magnitudes of around -500 K. correlation pattern exists between the present-day locations of cold masses in the lower mantle and the sites of past subduction since the Cretaceous. Results from correlation analysis show that the slab mass-flux in the lower mantle did not conform to a steady-state nature but exhibited time-dependent behavior.

Cadek, O.↗

NASA NTRS1993

Geophysical inferences of thermal-chemical structures in the lower mantle

Lateral variations of the temperature field in the lower mantle have been reconstructed using new results in mineral physics and seismic tomographic data. We show that, with the application of high-pressure experimental values of thermal expansivity and of sound velocities, the slow seismic anomalies in the lower mantle under the Pacific and Africa can be converted into realistic-looking plume structures with large dimensions of 0(1000 km). The outer fringes of the plumes have an excess temperature of around 400 K. In the core of the plumes are found tonguelike structures with extremely high thermal anomalies. These values can exceed 1200 K and are too high to be explained on the basis of thermal anomalies alone. We suggest that these major plumes in the deep mantle may be driven by both thermal and chemical buoyancies or that enhanced conductive heat-transfer may be important there.

Yuen, D. A.↗

NASA NTRS1993

Hard turbulent thermal convection and thermal evolution of the mantle

Hard turbulent convection is investigated using laboratory experiments and numerical simulations. In Newtonian mantle convection, the appearance of disconnected plumes marks the transition from soft to hard turbulence. For non-Newtonian rheology, the transition to hard turbulence takes place at much lower Nusselt numbers than it does for Newtonian rheology. This has important ramifications for the mantle. Large curvatures are developed in the trajectories of non-Newtonian plumes in the hard turbulent regime, in contrast to the trajectories of Newtonian plumes. When phase transitions are considered, mantle convection tends to become more layered with increasing Rayleigh numbers. The manner of mantle convection might have changed with time from a layered to a more whole mantle type of flow. Superplume events could have been caused by catastrophic overturns associated with strong gravitational instabilities in the transition zone.

Yuen, D. A.↗

NASA NTRS1993

Plume structures in the hard-turbulent regime of three-dimensional infinite Prandtl number convection

Numerical simulations of three-dimensional infinite Prandtl number thermal convection with Rayleigh number (Ra) up to 10 exp 8 are reported. Convection with Ra higher than 10 exp 7 is characterized by the appearance of disconnected thermal plumes. The smaller plumes are detached by the currents produced by the larger plumes. The low wavenumber portion of a thermal power spectrum near the boundary layer becomes flat at high Ra, while the spectrum measured in the interior shows a positive slope for low wavenumbers. Differences are found in the thermal spectra between 2D and 3D models.

Malevsky, A. V.↗

NASA NTRS1993

Three-dimensional instabilities of mantle convection with multiple phase transitions

The effects of multiple phase transitions on mantle convection are investigated by numerical simulations that are based on three-dimensional models. These simulations show that cold sheets of mantle material collide at junctions, merge, and form a strong downflow that is stopped temporarily by the transition zone. The accumulated cold material gives rise to a strong gravitational instability that causes the cold mass to sink rapidly into the lower mantle. This process promotes a massive exchange between the lower and upper mantles and triggers a global instability in the adjacent plume system. This mechanism may be cyclic in nature and may be linked to the generation of superplumes.

Honda, S.↗

NASA NTRS1993

Three-dimensional mantle dynamics with an endothermic phase transition

3D convection for the spinel to perovskite phase change has been simulated numerically. Results for Rayleigh (Ra) numbers of 0(10 exp 6) show intermittent layering with a strong robust plume rising through the phase boundary. Many descending instabilities are deflected but merging cold sheets come together at a junction. A pool of cold material accumulates underneath in the phase-transition zone. A strong gravitational instability results, which precipitates a rapid and massive discharge of upper-mantle material.

Honda, S.↗

NASA NTRS1992

Axisymmetric spherical shell models of mantle convection with variable properties and free and rigid lids

Axisymmetric spherical shell numerical simulations of mantle convection were carried out to investigate the influence of two end-member surface stress conditions: stress-free and rigid. These correspond approximately to a subducting or a rigid lithosphere and can be seen as end-member models of the surface of Venus. Our model assumed an effective Rayleigh number of 3 x 10 exp 6, similar to that for earth, and included uniform internal heating and depth-dependent thermal expansivity and thermal conductivity. The simulations utilized a Newtonian viscosity which was constant or varied with depth and/or temperature. We show how the temperature, speed, and vorticity fields change qualitatively and quantitatively with surface temperature, surface stress condition, internal heating and viscosity distribution. We find that a rigid lid and viscosity which increases with depth both promote steady large-scale circulation with smaller-scale circulation in the upper mantle.

Leitch, A. M.↗

NASA NTRS1992

Time-dependent three dimensional compressible convection with depth-dependent properties

Using a spectral code, we have studied the time-dependent regime of three-dimensional anelastic compressible convection with depth-dependent thermal expansivity, viscosity and thermal conductivity in a wide box of size 5 x 5 x 1. Surface Rayleigh numbers up to 5 x 10 exp 6 have been considered. Very few cylindrical plumes are developed at the bottom but they join up collectively to form strong upwellings, which pulsate chaotically. Major descending flows occur in sheets which form rectangular planform at the top. The thermal and flow fields are dominated by large-scale features. The bottom 20 percent of the convecting layer is found to be superadiabatic.

Balachandar, S.↗

NASA NTRS1992

Viscosity and thermal fields associated with strongly chaotic non-Newtonian thermal convection

The thermomechanical structure is investigated in strongly chaotic non-Newtonian thermal convection for both base-heated and internally-heated systems. Temperature can build up in stagnant regions and a non-Newtonian mantle can tolerate less internal heating. Viscosity fields of the strongly chaotic regime show a granular structure. The horizontal spectra of viscosity fluctuations obey a power-law and yield a fractal dimension of 1.6 to 1.8 for the isoviscosity lines, providing evidence for 2D turbulence. Long-wavelength viscosity variations are smoothed out by the turbulent non-Newtonian flows.

Malevsky, A. V.↗

NASA NTRS1992

The effects of Venusian mantle convection with multiple phase transitions

Recently there was a flurry of activities in studying the effects of phase transitions in the Earth's mantle. From petrological and geophysical considerations, phase-transitions would also play an important role in venusian dynamics. The basic differences between the two planets are the surface boundary conditions, both thermally and mechanically. In this vein we have studied time-dependent mantle convection with multiple phase transitions and depth-dependent thermal expansivity (alpha is approximately rho(exp -6)), based on high-pressure and temperature measurements. Both the olivine-spinel and spinel-perovskite transitions were simulated by introducing an effective thermal expansivity, as described. Used together with the extended Boussinesq Approximation this method serves as a powerful tool to examine the effects of phase transitions on convection at relatively low computational costs.

Steinbach, V.↗

NASA NTRS1992

Simulation of particle mixing by turbulent convective flows on the connection machine

Mixing of particles by chaotic flow fields was simulated on the Connection Machine. Each cell was assigned to the processor, and the coordinates of particles residing on the cell were kept in the local memory of the processor. This approach implies the exchange between the local memories, when a particle moves from one cell to another. Approximately 10 exp 5 particles were injected into a time-dependent flow field obtained by solving the nonlinear system of partial differential equations describing turbulent thermal convection. The flow field was calculated on a CRAY, and data were transferred to a CM-200 through a high-speed HIPPI channel.

Malevsky, A. V.↗

NASA NTRS1991

Characteristics-based methods applied to infinite Prandtl number thermal convection in the hard turbulent regime

Characteristics-based methods for the advection-diffusion equation are presented and directly applied to study thermal convection with extremely large Rayleigh number (Ra). It is shown that the operator-splitting method for advection-diffusion problems is very accurate for determining the advected field at extremely high Peclet number (Pe). The technique presented is considered to have great potential for solving advection-dominated problems, while the Langrangian method is more accurate for lower Pe. It is noted that the accuracy of these characteristics-based methods strongly depends on the quality of interpolation. The computational time for the operator-splitting method grows with the number of time steps employed. The Langrangian method was used for simulations of convection at very high Ra, up to 3 x 10 to the 9th, and time-dependent, thermal convection solutions were obtained for infinite Prandtl number.

Malevsky, A. V.↗

NASA NTRS1991

Compressible convection in a viscous Venusian mantle

Finite element simulations of axisymmetric spherical shell compressible convection were carried out to investigate the effect of various surface boundary conditions in a Venusian mantle, employing a thermal expansivity alpha which decreased with depth, a uniform viscosity an order of magnitude greater than the earth's, and zero and chondric quantities of internal heating. As long as hot plumes from the core-mantle boundary were strong, the convection pattern was typical of that for variable alpha flow; that is, it was characterized by steady upflowing regions, unsteady collections of downflowing plumes, and large aspect ratio cells. Increases in the internal heating or the temperature T0 at the top of the convecting layer weakened the hot plumes and, therefore, decreased the width of the cells. A rigid surface increased the internal temperature and also decreased the width of convection cells. Extensive regions of subadiabaticity were found in the mantle. These results are compared with those for fully three-dimensional convection under similar conditions (Schubert et al., 1990).

Leitch, A. M.↗

NASA NTRS1991

Development of diapiric structures in the upper mantle due to phase transitions

Solid-state phase transition in time-dependent mantle convection can induce diapiric flows in the upper mantle. When a deep mantle plume rises toward phase boundaries in the upper mantle, the changes in the local thermal buoyancy, local heat capacity, and latent heat associated with the phase change at a depth of 670 kilometers tend to pinch off the plume head from the feeding stem and form a diapir. This mechanism may explain episodic hot spot volcanism. The nature of the multiple phase boundaries at the boundary between the upper and lower mantle may control the fate of deep mantle plumes, allowing hot plumes to go through and retarding the tepid ones.

Liu, M.↗

NASA NTRS1991

Lower-mantle viscosity constrained by seismicity around deglaciated regions

It is shown here that seismicity around the margins of deglaciated areas provides a constraint on the viscosity of the lower mantle. Calculations using a spherical, viscoelastic earth model show that the present-day magnitude of the stress fields induced in the lithosphere beneath the Laurentide and Fennoscandian ice sheets is very sensitive to the value of the lower-mantle viscosity. Stress of about 100 bar, sufficient to cause seismicity, can still remain in the lithosphere for lower-mantle viscosities greater than about 10 to the 22nd Pa-s; for lower-mantle viscosities of about 10 to the 21st Pa-s, only a few tens of bars of stress persist in the lithosphere today. This influence of lower-mantle viscosity on the state of stress in the lithosphere also has implications for the migration of stress from earthquakes, and hence for earthquake recurrence times.

Spada, G.↗