Numerical studies of thermal convection with temperature- and pressure-dependent viscosity at extreme viscosity contrasts

Abstract

Motivated by convection of planetary mantles, we consider a mathematical model for Rayleigh-Bénard convection in a basally heated layer of a fluid whose viscosity depends strongly on temperature and pressure, defined in an Arrhenius form. The model is solved numerically for extremely large viscosity variations across a unit aspect ratio cell, and steady solutions for temperature, isotherms, and streamlines are obtained. To improve the efficiency of numerical computation, we introduce a modified viscosity law with a low temperature cutoff. We demonstrate that this simplification results in markedly improved numerical convergence without compromising accuracy. Continued numerical experiments suggest that narrow cells are preferred at extreme viscosity contrasts, and this conclusion is supported by a linear stability analysis. C 2015 AIP Publishing LLC. [http://dx

Constraints on plate tectonics initiation from scaling laws for single-cell convection

“…Previous studies have shown that convection is active in the top part of the convecting system (e.g., Christensen, 1984;Fleitout and Yuen, 1984;Christensen, 1985;Stemmer et al, 2006). At high viscosity contrasts the convective system divides to smaller sub-cells (Khaleque et al, 2015;Fowler et al, 2016), which can be interpreted as a reduction in the effective convective depth as we assume in this paper. Thus, it is important to consider pressure-dependent viscosity in the future studies of lithospheric failure.…”

<i>ConvectiveFoam1.0</i>: development and benchmarking of a infinite-Pr number solver

“…We remark that in this work we analyzed idealized models. This step is just the first of a longer project: further developments should consider rheological aspect of the Earth mantle such as the temperature/pressure viscosity dependence, which still has unsolved numerical issues in 3D domains (Khaleque et al, 2015). Also, analysis of both Newtonian and non Newtonian viscosity has to be considered.…”

“…For these reasons, indirect methods have usually been employed, such as seismic data analysis or numerical simulations. In particular, for the long time-scale behaviour (t τ M ), numerical simulations produce diagnostic and prognostic descriptions of geological processes (Khaleque et al, 2015). Furthermore, because of the high viscosity values (ν = 10 18 − 10 21 m 2 s −1 ), the infinite-Pr number assumption, where Pr = ν κ , ν is the kinematic viscosity and κ the thermal diffusivity, is usually adopted for the Earth mantle (Bercovici, 2007;Turcotte and Schubert, 2014).…”

Convection in the Earth-like Mantle with the Influence of Strong Viscosity Variation

“…Lenardic et al [9] discussed the depth dependence of viscosity for the mantle. Later dependence of viscosity on both temperature and pressure was examined by Shahraki and Schmeling [10], Khaleque et al [11]. The significant role of viscous dissipation in natural convection in vertical channels has been reported by Ostrach [12] and some others, whereas Gebhart [13] have studied its impact on vertical heated plates.…”