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

Balachandar, S.; Yuen, David A.; Reuteler, D.

doi:10.1029/92gl02146

Cited by 54 publications

(26 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A mantle depth of 2000 km is assumed in which the two major tions of mantle convection with both major phase transitions and discuss an instability (3) with Cartesian geometry because the radii of curvature of the Earth and those associated with phase changes differ by only 10%. We used the extended Boussinesq approximation (6,7,11,12) to model 3-D mantle convection with a thermal expansivity a(z) (1 3), an exponentially increasing viscosity q (z), and a thermal conductivity x(z), all of which depend on depth (1 4). This approximation has been shown in 2-D simulations to vield results (151 RaT (Rayleigh number) are based on surface values (18).…”

mentioning

confidence: 99%

Three-Dimensional Instabilities of Mantle Convection with Multiple Phase Transitions

Honda

Yuen

Balachandar

et al. 1993

Science

Self Cite

205

View full text Add to dashboard Cite

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.

show abstract

mentioning

confidence: 99%

Three-Dimensional Instabilities of Mantle Convection with Multiple Phase Transitions

Honda

Yuen

Balachandar

et al. 1993

Science

Self Cite

205

View full text Add to dashboard Cite

show abstract

“…However, because of the limitation of the computer power, many models were restricted to two-dimensional geometry. Recent availability of powerful computers makes tractable three-dimensional calculation in boxes (Cserepes et al, 1988;Houseman,, 1988;Travis et al, 1990;Balachandar et al, 1992;Honda et al, 1993) and in spherical shells (Baumgardner, 1985;Machetel et al, 1986;Glatzmaier, 1988;Bercovici et al, 1989Bercovici et al, , 1992Glatzmaier et al, 1990;Tackley et a1.,1993). However, since fully three-dimensional calculations in spherical shells need a large amount of the memory and computational time, they are still in a stage of development.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Infinite Prandtl Number Convection in a Spherical Shell with Temperature-Dependent Viscosity.

Iwase¹

1996

J. geomagn. geoelec

View full text Add to dashboard Cite

We study the numerical simulations of 3-D inifinite Prandtl number convection with temperaturedependent viscosity in a spherical shell. Control volume method coupled with SIMPLE algorithm is used to solve the basic equations. Both constant and temperature-dependent viscosity cases are studied under the condition that the ratio of the inner to the outer shell radius is 0.55, which is appropriate for mantle convection of the Earth, with only basal heating. For the case of constant viscosity, when the Rayleigh number (Ra) is less than 105, steady state solutions (both cubic and tetrahedral types) are obtained. However, forRa = 106, we find only a time-dependent solution. For the temperature-dependent viscosity case, we assume that the viscosity changes with temperature exponentially and we can successfully obtain solutions with the viscosity variation up to 10000. For the viscosity contrast of 1000 times and the surface Rayleigh number of Rao = 5 x 103, we get the flow patterns which consist of the sheet-like downwelling and small upwellings.

show abstract

“…To use the FEM on our mantle problem, first we note that Equation 12 can be rewritten as z~,~ -RaTk = 0 ( 2 1) where…”

Section: Finite-element Methodsmentioning

confidence: 99%

A numerical journey to the Earth's interior

King

1995

IEEE Comput. Sci. Eng.

View full text Add to dashboard Cite

HE INTERIOR OF THE EARTH HAS FASCINATED PHILOSOPHERS, PO-T ETS, and scientists throughout much of history. With the acceptance of the theory of plate tectonics in the last few decades, geologists now realize that some of the features we observe on the earth's surface have been formed by dynamic processes occurring deep within the planet's interior. Thus, understanding the inner workings of the earth has taken on new significance. Since we can't actually go down very deep into the earth, indirect observation combined with limited laboratory simulation of deep-earth conditions has had to suffice. These methods, in combination with increasingly sophisticated numerical models, tell us much of what we know about the inner dynamics of our planet.The dynamics of the earth's mantle-the layer that makes up the majority of the earth's volume-can be modeled using the equations that govern a creeping, viscous fluid. While on a human time scale the earth seems like a rigd, elastic body, over millions of years it responds to stresses by creeping flow. This behavior is similar to the more familiar movement of glaciers. Two of the problems faced by geophysicists in modeling the earth's interior are the variation in the material properties of the mantle and the range of length scales of the phenomenon they want to study. To study the problems currently of interest to geologists requires three-dimensional, spherical shell models that can resolve details on the order of several kilometers. This is beyond the CPU and memory limitations of almost all computers available today. In addition, the large variation in the material properties of mantle materials causes most numerical algorithms to become unstable.To model the dynamic behavior of the earth's interior, we must first know something about its composition. Our knowledge is considerable but far from perfect: many of the material parameters are only poorly constrained by laboratory and other measurements. It is useful to note in passing that numerical modeling can help to test the sensitivity of the earth's interior dynamics to the unknown parameters, guiding experimentalists toward better measurements of the key properties that control the dynamics. 1070-9924/95/$4 00 0 1995 IEEE IEEE COMPUTATIONAL SCIENCE h ENGINEERING BEST COW AVAILABLB , \

show abstract

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

Cited by 54 publications

References 14 publications

Three-Dimensional Instabilities of Mantle Convection with Multiple Phase Transitions

Three-Dimensional Instabilities of Mantle Convection with Multiple Phase Transitions

Three-Dimensional Infinite Prandtl Number Convection in a Spherical Shell with Temperature-Dependent Viscosity.

A numerical journey to the Earth's interior

Contact Info

Product

Resources

About