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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 18:03:33 +0000Finite Element Solution of Thermal Convection On A Hypercube
Concurrent Computer
https://resolver.caltech.edu/CaltechAUTHORS:20121119-131724167
Authors: Gurnis, Michael; Raefsky, Arthur; Lyzenga, Gregory A.; Hager, Bradford H.
Year: 1988
DOI: 10.1145/63047.63070
Numerical solutions to thermal convection flow problems
are vital to many scientific and engineering problems.
One fundamental geophysical problem is the thermal convection
responsible for continental drift and sea floor
spreading. The earth's interior undergoes slow creeping
flow (~cm/yr) in response to the buoyancy forces generated
by temperature variations caused by the decay of
radioactive elements and secular cooling. Convection in
the earth's mantle, the 3000 km thick solid layer between
the crust and core, is difficult to model for three reasons:
(1) Complex rheology -- the effective viscosity depends
exponentially on temperature, on pressure (or depth) and
on the deviatoric stress; (2) the buoyancy forces driving
the flow occur in boundary layers thin in comparison to the
total depth; and (3) spherical geometry -- the flow in the
interior is fully three dimensional. Because of these many
difficulties, accurate and realistic simulations of this process
easily overwhelm current computer speed and memory
(including the Cray XMP and Cray 2) and only simplified
problems have been attempted [e.g. Christensen and
Yuen, 1984; Gurnis, 1988; Jarvis and Peltier, 1982].
As a start in overcoming these difficulties, a number of
finite element formulations have been explored on hypercube
concurrent computers. Although two coupled equations
are required to solve this problem (the momentum
or Stokes equation and the energy or advection-diffusion
equation), we will concentrate our efforts on the solution
to the latter equation in this paper. Solution of the former
equation is discussed elsewhere [Lyzenga, et al, 1988].
We will demonstrate that linear speedups and efficiencies
of 99 percent are achieved for sufficiently large problems.https://authors.library.caltech.edu/records/rke4a-npe19Constraints on the Structure of Mantle Convection Using Seismic Observations, Flow Models, and the Geoid
https://resolver.caltech.edu/CaltechAUTHORS:20121002-141328164
Authors: Hager, Bradford H.; Clayton, Robert W.
Year: 1989
The establishment of the theory of plate tectonics in the late 1960s has left
little doubt that the mantle is convecting. The plates themselves form the cold
upper thermal boundary layer of the mantle convection system; the cooling of
oceanic plates as they move away from midoceanic ridges provides the
mechanism by which the Earth loses most of its heat (e.g., Sclater et al.,
1980; O'Connell and Hager, 1980). The mantle is in turn cooled by the cold
slabs that plunge into Earth's interior at subduction zones.
Although plate tectonics implies that convective motions in the mantle are
the dominant mechanism for heat transport, and we can measure the surface
motions associated with it, we are remarkably ignorant of even the gross
features of the interior flow field associated with this mantle circulation. Only
at subduction zones, where seismicity presumably marks the particle trajectories
of the cold descending boundary layer, do we have direct evidence for
the interior flow pattern and state of stress. Most of what is understood, or
thought to be understood, about convection in the Earth's interior is based on
comparison of simplified models to observations taken at the surface.
Examples of these models of mantle convection are given in the other
chapters of this book, as well as in the general geophysical literature. These
include studies of convection in media with uniform rheology (Busse, this
volume; Jarvis and Peltier, this volume), interpretation of travel time anomalies
from deep earthquakes in terms of simple thermal models of subducted
slabs (Jordan eta!., this volume), interpretation of geochemical anomalies in
terms of models of the distribution of mantle heterogeneities (Hart and
Zindler, this volume), and interpretation of changes in the Earth's shape and
rotational parameters in terms of models of mantle rheology (Peltier, this
volume).
In order to be useful, models must be simple enough to understand, and
yet contain enough of the essential physics to be applicable. The line
between oversimplification and overwhelming complexity is a fine one, and
its positioning is a matter of subjective judgement, particularly when some
observations have a fairly small signal to noise ratio. The ultimate test of a
particular model is whether it can satisfy, within their uncertainties, the
observations. If it cannot it must be rejected, although unfortunately, the
converse is not true. The more types of observations a model can satisfy,
however, the more likely it is to be correct.https://authors.library.caltech.edu/records/n21w7-jrw19Topographic Core-Mantle Coupling and Fluctuations in the Earth's Rotation
https://resolver.caltech.edu/CaltechAUTHORS:20121016-145941398
Authors: Hide, R.; Clayton, R. W.; Hager, B. H.; Spieth, M. A.; Voorhdes, C. V.
Year: 1993
DOI: 10.1029/GM076p0107
Astronomically-determined irregular fluctuations in the Earth's rotation vector on decadal time scales can be used to estimate the fluctuating torque on the lower surface of the Earth's mantle produced by magnetohydrodynamic flow in the underlying liquid metallic core. A method has been proposed for testing the hypothesis that the torque is due primarily to fluctuating dynamic pressure forces acting on irregular topographic features of the core-mantle boundary and also on the equatorial bulge. The method exploits (a) geostrophically-constrained models of fluid motions in the upper reaches of the core based on geomagnetic secular variation data, and (b) patterns of the topography of the CMB based on the mantle flow models constrained by data from seismic tomography, determinations of long wave-length anomalies of the Earth's gravitational field and other geophysical and geodetic data. According to the present study, the magnitude of the axial component of the torque implied by determinations of irregular changes in the length of the day is compatible with models of the Earth's deep interior characterized by the presence of irregular CMB topography of effective "height" no more than about 0.5 km (about 6% of the equatorial bulge) and strong horizontal variations in the properties of the Dâ€³ layer at the base of the mantle. The investigation is now being extended to cover a wider range of epochs and also the case of polar motion on decadal time scales produced by fluctuations in the equatorial components of the torque.https://authors.library.caltech.edu/records/k00cv-6cf89