The characteristics of thermal convection in a fluid whose viscosity varies strongly with temperature are studied in the laboratory. At the start of an experiment, the upper boundary of an isothermal layer of Golden Syrup is cooled rapidly and maintained at a fixed temperature. The fluid layer is insulated at the bottom and cools continuously. Rayleigh numbers calculated with the viscosity of the well-mixed interior are between 106 and 108 and viscosity contrasts are up to 106. Thermal convection develops only in the lower part of the thermal boundary layer, and the upper part remains stagnant. Vertical profiles of temperature are measured with precision, allowing deduction of the thickness of the stagnant lid and the convective heat flux. At the onset of convection, the viscosity contrast across the unstable boundary layer has a value of about 3. In fully developed convection, this viscosity contrast is higher, with a typical value of 10. The heat flux through the top of the layer depends solely on local conditions in the unstable boundary layer and may be written \[Q_{\rm s} = - CK_{\rm m} (\alpha g/\kappa \nu_{\rm m})^{\frac{1}{3}} \Delta T^{\frac{4}{3}}_{\rm v}\], where km and νm are thermal conductivity and kinematic viscosity at the temperature of the well-mixed interior, κ thermal diffusivity, α the coefficient of thermal expansion, g the acceleration due to gravity. ΔTv, is the ‘viscous’ temperature scale defined by \[\Delta T_{\rm v} = - \frac{\mu (T_{\rm m})}{({\rm d}\mu /{\rm d}T)(T_{\rm m})}\] where μ(T) is the fluid viscosity and Tm the temperature of the well-mixed interior. Constant C takes a value of 0.47 ± 0.03. Using these relations, the magnitude of temperature fluctuations and the thickness of the stagnant lid are calculated to be in excellent agreement with the experimental data. One condition for the existence of a stagnant lid is that the applied temperature difference exceeds a threshold value equal to (2ΔTv).

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112093001740

Transient high-Rayleigh-number thermal convection with large viscosity variations

Heat flow measurements through old seafloor demonstrate that the oceanic lithosphere is heated from below away from hot spot tracks. We reevaluate the hypothesis of small-scale convection beneath the lithosphere with laboratory experiments in fluids whose viscosity depends strongly on temperature. Rayleigh numbers were between 106 and 108 and viscosity contrasts were up to 106. A layer of fluid was impulsively cooled from above, and a cold boundary layer grew at the top of the fluid layer. After a finite time, convective instabilities developed in the lowermost part of the boundary layer, while the upper part remained stagnant. The variation of surface heat flow as a function of time reflects the three-dimensional nature of the flow and the presence of a thick lid. At viscosity contrasts greater than 103, this variation is very similar to what is observed on the oceanic lithosphere. For small times, heat flow follows the behavior of a half-space cooled from above by conduction. Some time after the onset of convection, it deviates from the conductive evolution and settles to a value which seems almost constant over a length of time equal to a few multiples of the onset time. The occurrence of small-scale convection is difficult to detect in global data sets of seafloor depths. The onset of convection is marked by a small “trough” in the local subsidence curve but does not occur at the same time everywhere because of the probabilistic nature of the instability process. Later instabilities occur independently of each other and, at any given age, involve a region of small horizontal extent below a thick lid. The characteristics of the instability depend on the function describing the variation of viscosity with temperature. Scaling laws are derived for the onset time and for the surface heat flow. The requirement that small-scale convection supplies 45 mW m−2 to the oceanic lithosphere provides a relationship between the activation enthalpy for creep and the asthenosphere viscosity. For a range of activation enthalpy of 250 to 600 kJ mol−1, the asthenosphere viscosity must be between 3×1018 and 4×1017 Pa s. The thickness of the stagnant lid and the temperature difference driving small-scale convection are predicted to be about 80 km and 200°C, respectively.

Onset of thermal convection in fluids with temperature‐dependent viscosity: Application to the oceanic mantle

On Convective Style and Vigor in Sheet-like Magma Chambers

[1] We investigate the physics of multiscale convection in Earth's mantle, characterized by the coexistence of large-scale mantle circulation associated with plate tectonics and small-scale sublithospheric convection. In part 2 of our study, the temporal and spatial evolution of sublithospheric convection is studied using two-dimensional whole mantle convection models with temperature- and depth-dependent viscosity and an endothermic phase transition. Scaling laws for the breakdown of layered convection as well as the strength of convection are derived as a function of viscosity layering, the phase buoyancy parameter, and the thermal Rayleigh number. Our results suggest that layered convection in the upper mantle is maintained only for a couple of overturns, with plausible mantle values. Furthermore, scaling laws for the onset of convection, the stable Richter rolls, and the breakdown of layered convection are all combined to delineate possible dynamic regimes beneath evolving lithosphere. Beneath long-lived plates, the development of longitudinal convection rolls is suggested to be likely in the upper mantle, as well as its subsequent breakdown to whole mantle-scale convection. This evolutionary path is suggested to be consistent with the seismic structure of the Pacific upper mantle.

/pdf/physics-of-multiscale-convection-in-earth-s-mantle-evolution-2qy8lg07qx.pdf

Physics of multiscale convection in Earth's mantle: Evolution of sublithospheric convection

https://people.earth.yale.edu/sites/default/files/korenaga04b.pdf

Mantle mixing and continental breakup magmatism

Onset times for convection induced by buoyancy forces have been measured. Results on three aqueous systems are summarized in terms of a critical value for a time-dependent Rayleigh number. Because of the presence of minute traces of unavoidable surface-active contaminants, a ‘free’ water surface behaved as if it were inflexible and laterally rigid so far as determining first convective motion was concerned. The form of the onset motion was observed with schlieren photography for both top and side view. The pattern at onset was frequently in the form of plunging rings. Surface effects were demonstrated with an organic liquid layer in which onset times were measured for convection driven by surface tension gradients as well as by buoyancy forces. The data are compared with some recent predictions of linear stability analyses.

L. M. Blair

Papers

The onset of cellular convection in a fluid layer with time-dependent density gradients