Parametrization of heat transport by non-Newtonian convection

Kawada, Yoshitaka; Honda, Sawao

doi:10.1046/j.1365-246x.1999.00795.x

Cited by 6 publications

(3 citation statements)

References 18 publications

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“…This thickness is less than the 310 km expected from equation (15) for nonlinear convection (n = 5 in equation (15)). This discrepancy occurs because the convection in the model is very time-dependent, like convection (without basal drag) cooled from above in a fluid with a nonlinear viscosity [Solomatov, 1995;Reese et al, 1998Reese et al, , 1999Kawada and Honda, 1999;Solomatov andMoresi, 1997, 2000]. That is, the thermal boundary layer is stagnant at most times.…”

Section: Parameterized Convection With Strong Basal Dragmentioning

confidence: 99%

Survival of Archean cratonal lithosphere

2003

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[1] I use thermal convection models to search for combinations of physical parameters that are compatible with the results of xenolith studies on the history and present thermal structure of cratonal lithosphere. The cratonal lithosphere above $180 km depth formed in the Archean and remained stable until recently sampled. The mantle adiabat cooled $150 K over this time. The temperature change across the rheologically active boundary layer at the lithospheric base is <300 K over a depth range of several tens of kilometers. Modern cratonal lithospheric thicknesses are relatively uniform, $225 km, much thicker than old oceanic lithosphere. Cratonal lithosphere is now in quasi-steady state with conductive heat flow to the surface in balance with heat supplied to the base of the lithosphere by convection driven by local temperature contrasts within the rheologically active boundary layer. This heat flow and the lithosphere thickness changed little after the cratonal lithosphere stabilized. One possibility is that chemically buoyant lithosphere forms a conductive lid above the convecting normal mantle. To survive, the chemical lithosphere also needs to be more viscous than normal mantle. A reasonable situation has chemical lithosphere a factor of 20 more viscous than normal mantle with weakly temperature-dependent viscosity (a factor of e over 100 K) from 0.2 Â 10 20 Pa s along the modern mantle adiabat. However, a chemical lid is unnecessary for lithospheric thickness to change slowly over time. For example, the base of the lithosphere may be stable if the viscosity at its base (along an adiabat) decreases rapidly with depth.

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Section: Parameterized Convection With Strong Basal Dragmentioning

confidence: 99%

Survival of Archean cratonal lithosphere

2003

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“…On the Earth it occurs as secondary convection beneath the plates and transfers moderate amounts of heat to the oceanic lithosphere [Davaille and Jaupart, 1994] where k is thermal conductivity, p is density, g is the acceleration of gravity, cz is the thermal expansion coefficient, r-=k/pC is thermal diffusivity, ri0 is the half-space viscosity, T n is the temperature to change viscosity by a factor of e, and pC is specific heat per volume. The temperature contrast across the boundary layer is 2 T n to 3 T n. Kawada and Honda, 1999]. Crudely, nonlinear fluid is nearly equivalent to a linear fluid with an apparent T n a factor of n larger than the actual T n. More precise parameterizations are complicated and are not repeated here.…”

Section: Modes Of Convectionmentioning

confidence: 99%

Evolution of the mode of convection within terrestrial planets

Sleep¹

2000

J. Geophys. Res.

188

135

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Abstract. Magma oceans, plate tectonics, and stagnant-lid convection have transferred heat out of the terrestrial planets at various times in their histories. The implications of the existence of multiple branches are graphically illustrated by approximating the globally averaged mantle heat flow as a function of the interior potential temperature. For this assumption to be valid, the mantle heat flow needs to be able to change rapidly relative to the potential temperature, or, equivalently, lithosphere needs to be a small fraction of the mass planet. This criterion is satisfied by the Earth, Venus, and Mars, but not the Moon. At a given potential temperature the function may be multivalued with a separate branch representing each mode of convection. The heat flow evolves along a branch as the potential temperature changes depending on whether the heat flow is greater or less than the global radioactive heat generation. When the end of a branch is reached, the state of the system jumps to another branch, quickly changing the global heat flow. Examples include transitions from a magma ocean to plate tectonics, probably on the Earth and Mars, and conceivably Venus; and the transition from a stagnant-lid planet to a magma ocean on Venus and the eventual return to a stagnant-lid planet.

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“…Eq. 27has also been used by Christensen (1984), who found l = 1 also to be a suitable choice, as we well as by Kawada & Honda (1999). Independent of the method used, we always exclude the stagnant lid upon averaging the viscosity.…”

Section: Nusselt-rayleigh Scalingmentioning

confidence: 99%

Stagnant-lid convection with diffusion and dislocation creep rheology: Influence of a non-evolving grain size

Schulz

Tosi

Plesa

et al. 2019

Geophysical Journal International

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SUMMARY Heat transfer in one-plate planets is governed by mantle convection beneath the stagnant lid. Newtonian diffusion creep and non-Newtonian dislocation creep are the main mechanisms controlling large-scale mantle deformation. Diffusion creep strongly depends on the grain size (d), which in turn controls the relative importance of the two mechanisms. However, dislocation creep is usually neglected in numerical models of convection in planetary mantles. These mostly assume linear diffusion creep rheologies, often based on reduced activation parameters (compared to experimental values) that are thought to mimic the effects of dislocation creep and, as a side benefit, also ease the convergence of linear solvers. Assuming Mars-like parameters, we investigated the influence of a non-evolving grain size on Rayleigh–Bénard convection in the stagnant lid regime. In contrast to previous studies based on the Frank–Kamentskii approximation, we used Arrhenius laws for diffusion and dislocation creep—including temperature as well as pressure dependence—based on experimental measurements of olivine deformation. For d ≲ 2.5 mm, convection is dominated by diffusion creep. We observed an approximately equal partitioning between the two mechanisms for d ≈ 5 mm, while dislocation creep dominates for d ≳ 8 mm. Independent estimates of an average grain size of few mm up to 1 cm or more for present-day Mars suggest thus that dislocation creep plays an important role and possibly dominates the deformation. Mimicking dislocation creep convection using an effective linear rheology with reduced activation parameters, as often done in simulations of convection and thermal evolution of Mars, has significant limitations. Although it is possible to mimic mean temperature, mean lid thickness and Nusselt number, there are important differences in the flow pattern, root mean square velocity, and lid shape. The latter in particular affects the amount and distribution of partial melt, suggesting that care should be taken upon predicting the evolution of crust production when using simplified rheologies. The heat transport efficiency expressed in terms of the Nusselt number as a function of the Rayleigh number is thought to depend on the deformation mechanisms at play. We show that the relative volume in which dislocation creep dominates has nearly no influence on the Nusselt–Rayleigh scaling relation when a mixed rheology is used. In contrast, the flow pattern influences the Nusselt number more strongly. We derived a scaling law for the Nusselt number based on the mean lid thickness (〈L〉) and on the effective Rayleigh number (Raeff) obtained by suitably averaging the viscosity beneath the stagnant lid. We found that the Nusselt number follows the scaling $\mathrm{Nu} = 0.37 \langle L \rangle ^{-0.666} \mathrm{Ra}_{\mathrm{eff}}^{0.071}$ regardless of the deformation mechanism.

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Parametrization of heat transport by non-Newtonian convection

Cited by 6 publications

References 18 publications

Survival of Archean cratonal lithosphere

Survival of Archean cratonal lithosphere

Evolution of the mode of convection within terrestrial planets

Stagnant-lid convection with diffusion and dislocation creep rheology: Influence of a non-evolving grain size

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