A benchmark study on mantle convection in a 3‐D spherical shell using CitcomS

Abstract

[1] As high-performance computing facilities and sophisticated modeling software become available, modeling mantle convection in a three-dimensional (3-D) spherical shell geometry with realistic physical parameters and processes becomes increasingly feasible. However, there is still a lack of comprehensive benchmark studies for 3-D spherical mantle convection. Here we present benchmark and test calculations using a finite element code CitcomS for 3-D spherical convection. Two classes of model calculations are presented: the Stokes' flow and thermal and thermochemical convection. For Stokes' flow, response functions of characteristic flow velocity, topography, and geoid at the surface and core-mantle boundary (CMB) at different spherical harmonic degrees are computed using CitcomS and are compared with those from analytic solutions using a propagator matrix method. For thermal and thermochemical convection, 24 cases are computed with different model parameters including Rayleigh number (7 Â 10 3 or 10 5 ) and viscosity contrast due to temperature dependence (1 to 10 7 ). For each case, time-averaged quantities at the steady state are computed, including surface and CMB Nussult numbers, RMS velocity, averaged temperature, and maximum and minimum flow velocity, and temperature at the midmantle depth and their standard deviations. For thermochemical convection cases, in addition to outputs for thermal convection, we also quantified entrainment of an initially dense component of the convection and the relative errors in conserving its volume. For nine thermal convection cases that have small viscosity variations and where previously published results were available, we find that the CitcomS results are mostly consistent with these previously published with less than 1% relative differences in globally averaged quantities including Nussult numbers and RMS velocities. For other 15 cases with either strongly temperature-dependent viscosity or thermochemical convection, no previous calculations are available for comparison, but these 15 test calculations from CitcomS are useful for future code developments and comparisons. We also presented results for parallel efficiency for CitcomS, showing that the code achieves 57% efficiency with 3072 cores on Texas Advanced Computing Center's parallel supercomputer Ranger.

A linear stability analysis on the onset of thermal convection of a fluid with strongly temperature-dependent viscosity in a spherical shell

“…Indeed, as can be seen in Fig. 14a, the changes in the vertical structures of incipient flows occur at around r η 10 4 (i.e., E 9.2), while, from earlier numerical studies [2,28,31], that the collapse of the SL-mode of convection occurs at the values of r η larger than 10 4 . It can, therefore, be conjectured that, for a range of 10 4 r η 10 4.5 , there exists an ST-mode of convection with convection cells of large horizontal length scales.…”

“…14a, the classification of convective regimes, inferred from the changes in the horizontal length scales of convection cells, obtained by earlier numerical experiments of thermal convection in three-dimensional spherical shells [2,13,18,28,31]. Among the symbols in the figure, the triangles indicate the conditions for a so-called "sluggish-lid" (SL) mode of convection which is characterized by convection cells of large horizontal scales (see Fig.…”

“…We also note that, on the other hand, . Circles, triangles, and squares indicate that convective patterns with narrow, wide, and again narrow cells have been reported in earlier studies with increasing r η , respectively; black symbols from [28], blue symbols from [18], green symbols from [31], and red symbols from [2]. For γ = 0.55, in contrast, the values of Ra 2 * c0 moderately vary depending on E with a gradual increase for large E, since the aspect ratio γ 2c0 of the sublayer significantly increases with increasing E for a thick spherical shell.…”

Drift of Plumes in the Mantle

“…The governing equations may be nondimensionalized as in the work of Zhong et al (2000) and Zhong et al (2008) via:…”

“…However, Courtillot et al (2003) have collected various lines of evidence to support the existence of multiple possible sources of thermal plumes in the mantle. These include geochemical contrasts of 3 He/ 4 He and 21 Ne/ 22 Ne ratios between mid-ocean ridge basalts (MORBs) and ocean island basalts (OIBs), correlation of Large Igneous Provinces (LIPs) with impinging mantle plume heads, laboratory studies of thermal convection in viscous fluids [Whitehead and Luther, 1975;Jellinek and Manga, 2004], numerical convection studies [Steinberger and O'Connell, 1998;Zhong et al, 2000, Zhong et al, 2001McNamara and Zhong, 2004;Zhong et al, 2008], and seismic imaging of the deep mantle beneath Hawaii and Iceland [Wolfe et al, 1997]. Sleep (2006) has also investigated the origins of plumes using first principles and found that thermal boundary layers at the core-mantle boundary and 410-670 km transition zone result in thermal instabilities which generate thermal upwellings.…”