Effective buoyancy ratio: a new parameter for characterizing thermo-chemical mixing in the Earth's mantle

Galsa, Attila; Herein, Mátyás; Lenkey, László; Farkas, Márton Pál; Taller, G.

doi:10.5194/se-6-93-2015

Cited by 5 publications

(4 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An application of the above to the Earth's mantle [35][36][37] with parameters d ≈ 2900 km, κ ≈ 10 −6 m 2 /s, Ra ≈ 5 × 10 7 , Pr ≈ 10 23 − 10 24 , and U ≈ 20 mm/yr yields (Pe) obs ≈ 1840, which is close to our prediction that (Pe) theory ≈ 1580.…”

Section: Resultssupporting

confidence: 80%

“…The other limiting case (viscous regime), c 2 4 Pr 2 4c 3 (c 1 − c 2 )RaPr, yields Pe = (c 3 /c 4 )Ra ≈ 0.0375Ra 0.61 , which is independent of Pr as observed in several numerical simulations and experiments [13,19,24,29,30]. An application of the above to the Earth's mantle [35][36][37] with parameters d ≈ 2900 km, κ ≈ 10 −6 m 2 /s, Ra ≈ 5 × 10 7 , Pr ≈ 10 23 − 10 24 , and U ≈ 20 mm/yr yields (Pe) obs ≈ 1840, which is close to our prediction that (Pe) theory ≈ 1580.…”

Section: Resultsmentioning

confidence: 93%

See 1 more Smart Citation

Dynamics of large-scale quantities in Rayleigh-Bénard convection

et al. 2016

View full text Add to dashboard Cite

In this paper we estimate the relative strengths of various terms of the Rayleigh-Bénard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity, U , or the Péclet number that is applicable for arbitrary Rayleigh number Ra and Prandtl number Pr. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling from the theoretical prediction of Ra 1/2 to the experimentally observed scaling of nearly Ra 0.3 .

show abstract

Section: Resultssupporting

confidence: 80%

Section: Resultsmentioning

confidence: 93%

Dynamics of large-scale quantities in Rayleigh-Bénard convection

et al. 2016

View full text Add to dashboard Cite

show abstract

“…In this way Ra CR changes between 1.7 9 10 3 and 1.7 9 10 4 in different simulations. Based on the results obtained from seismic tomography, thermo-chemical model calculations and normal modes of the Earth (Koelemeijer et al 2012;Ishii and Tromp 2004;Tackley 2012;Galsa et al 2015) b = 2-4 % might be a reasonable value for the LLSVP. The evolution of the equatorial surface elevation shows an exponentional relaxation to an equilibrium state in every case.…”

Section: Theoretical Background and Model Descriptionmentioning

confidence: 98%

Numerical evolution of the asymmetry in the compositionally inhomogeneous lower mantle driven by Earth’s rotation

2016

View full text Add to dashboard Cite

Numerical model calculations have been carried out to study the effect of the centrifugal force on the compositionally dense material accumulated in the lowermost mantle. The deformation of an initial dense layer encircling the core was investigated systematically as a function of the density difference between the lower dense and the overlaying mantle, b and the angular velocity of the planet, X in a two-dimensional cylindrical shell domain. It was established that increasing b does not influence the magnitude of the deformation of the dense layer but decreases the velocity of the deformation. The relaxation time of the deformation is inversely proportional to b similarly to post-glacial rebound. On the other hand, increasing X enhances the magnitude of the deformation but does not affect the deformation relaxation time. The magnitude of the deformation is approximately proportional to X 2 . It was pointed out that for the present-day mantle parameters, b = 2-4 % and X = 7.3 9 10 -5 1/s the equatorial elevation of the dense layer is about 2 km which more than two orders of magnitude less than the height of the seismically observed large low shear velocity provinces beneath Africa and Pacific. During the Earth's history when the rotation of our planet was faster the influence of the centrifugal force was much more significant and the equatorial elevation of the dense layer might have reached even 100 km.

show abstract

“…A number of studies of the role of compositional discontinuities on mantle convection have been carried out. Numerical studies include [29], [26], [43], and [11]. [7] has carried out an extensive laboratory studies.…”

Section: Introductionmentioning

confidence: 99%

New numerical approaches for modeling thermochemical convection in a compositionally stratified fluid

Puckett

Turcotte

et al. 2018

Physics of the Earth and Planetary Interiors

View full text Add to dashboard Cite

Seismic imaging of the mantle has revealed large and small scale heterogeneities in the lower mantle; specifically structures known as large low shear velocity provinces (LLSVP) below Africa and the South Pacific. Most interpretations propose that the heterogeneities are compositional in nature, differing in composition from the overlying mantle, an interpretation that would be consistent with chemical geodynamic models. The LLSVP's are thought to be very old, meaning they have persisted throughout much of Earth's history. Numerical modeling of persistent compositional interfaces presents challenges, even to state-of-the-art numerical methodology. For example, some numerical algorithms for advecting the compositional interface cannot maintain a sharp compositional boundary as the fluid migrates and distorts with time dependent fingering due to the numerical diffusion that has been added in order to maintain the upper and lower bounds on the composition variable and the stability of the advection method. In this work we present two new algorithms for maintaining a sharper computational boundary than the advection methods that are currently openly available to the computational mantle convection community; namely, a Discontinuous Galerkin method with a Bound Preserving limiter (DGBP) and a Volume-of-Fluid (VOF) interface tracking algorithm. We compare these two new methods with two approaches commonly used for modeling the advection of two distinct, thermally driven, compositional fields in mantle convection problems; namely, an approach based on a high-order accurate finite element method (FEM) advection algorithm that employs an artificial viscosity technique known as 'Entropy Viscosity' (FEM-EV) to maintain the upper and lower bounds on the composition variable as well as the stability of the advection algorithm and the advection of particles that carry a scalar quantity representing the location of each compositional field. All four of these algorithms are implemented in the open source FEM code ASPECT, which we use to compute the velocity, pressure, and temperature fields associated with the underlying flow field. We compare the performance of these four algorithms by computing the solution to an initially compositionally stratified fluid that is subject to a thermal gradient at a Rayleigh number of Ra = 10 5 with a buoyancy ratio of B = 1.0. For B = 1.0, a value for which the initial stratification of the compositional fields persists indefinitely, our computations demonstrate that the entropy viscosity-based method has far too much numerical diffusion to yield meaningful results. On the other hand, the DGBP method yields good results, although small amounts of each compositional field are numerically entrained within the other compositional field. The particle method yields yet better results than this, but some particles representing the denser fluid are entrained in the upper, less dense fluid and are advected to the top of the computational domain and, similarly, particles representing the less d...

show abstract

Effective buoyancy ratio: a new parameter for characterizing thermo-chemical mixing in the Earth's mantle

Cited by 5 publications

References 47 publications

Dynamics of large-scale quantities in Rayleigh-Bénard convection

Dynamics of large-scale quantities in Rayleigh-Bénard convection

Numerical evolution of the asymmetry in the compositionally inhomogeneous lower mantle driven by Earth’s rotation

New numerical approaches for modeling thermochemical convection in a compositionally stratified fluid

Contact Info

Product

Resources

About