Modelling planetary dynamics by using the temperature at the core–mantle boundary as a control variable: effects of rheological layering on mantle heat transport

Abstract

In planetary convection, there has been a great emphasis laid on the usage of the Rayleigh number as a control parameter for describing the vigor of convection. However, realistic mantle rheology not only depends on temperature, pressure, strain-rate and composition, but also on the nature of the dominant creep mechanism, which varies with pressure and also with temperature. It is difficult to study the effects of varying influences from the convective strength without also changing the mantle flow law in the process. We have adopted the approach of using as the sole control parameter, the temperature at the core-mantle boundary, T , in modelling planetary dynamics with a composite non-Newtonian and Newtonian CMB rheology, which is temperature-dependent in the upper mantle and both temperature-and pressure-dependent in the lower mantle. Increasing the T strengthens convective vigor and leads to a non-linear increase of averaged temperature, CMB heat-flow and root-mean-squared velocity. The interior viscosity decreases strongly with T and internal heating due to CMB radioactivity. A viscosity maximum is found in the horizontally averaged viscosity profile at a depth around 2000 km. This viscosity hill moves downward with diminishing amplitude in the face of increasing dissipation number and internal heating. The bottom third of the lower mantle appears to be superadiabatic as a consequence of the stiff lower-mantle rheology. The Ž . scaling relationship between the Nusselt Nu number and T shows a relatively insensitive increase of Nu with T . In CMB CMB Ž . terms of an effective Rayleigh number of the whole system, Ra , the power-law exponent of the Nu Ra relationship is E E very low, around 0.12. Strong pressure-dependence of lower-mantle rheology and its large volume relative to the entire mantle would induce a much lower cooling rate of the planet than previous models based on parameterized convection with a temperature-dependent viscosity. q

Urey ratio and the structure and evolution of Earth's mantle

“…Whereas the average viscosity of deeper mantle under present‐day conditions can be inferred from geophysical observations such as the geoid and postglacial rebound [e.g., Hager et al , 1985; Mitrovica and Forte , 1997], its temperature dependency must be estimated through experimental studies, which are still difficult to conduct at lower mantle conditions [e.g., Karato et al , 1995]. Also, we can only speculate at this point how different deformation mechanisms, such as diffusion and dislocation creep, might compete in the lower mantle [ Karato , 1998], and van den Berg and Yuen [1998] suggested that, under certain conditions, heat flow scaling for the lower mantle may resemble that of Christensen [1985a]. Alternatively, Solomatov [1996] suggested that if the lower mantle is mainly deformed by diffusion creep, which is known to be very sensitive to grain size, the kinetics of grain growth may reverse the temperature dependency of lower mantle viscosity; that is, hotter mantle may become stiffer because grains would grow faster at higher temperatures.…”

A thermo-mechanical model of horizontal subduction below an overriding plate

“…The applied mantle rheology is based on a composite rheological model combining both Newtonian and non-Newtonian £ow, corresponding to di¡usion and dislocation creep respectively [14,27,29,30]. We use an Arrhenius relation for each of the £ow components for both mantle and crustal materials :…”

Interaction between small‐scale mantle diapirs and a continental root

“…can be transformed into a viscosity expression [see van den Berg and Yuen , 1998]: For values of n unequal to unity, η k introduces a nonlinearity through in the momentum [ van den Berg et al , 1993].…”