Anne Davaille

Three distinct types of hotspots in the Earth's mantle

The origin of mantle hotspots is a controversial topic. Only seven (‘primary’) out of 49 hotspots meet criteria aimed at detecting a very deep origin (three in the Pacific, four in the Indo-Atlantic hemisphere). In each hemisphere these move slowly, whereas there has been up to 50 mm/a motion between the two hemispheres prior to 50 Ma ago. This correlates with latitudinal shifts in the Hawaiian and Reunion hotspots, and with a change in true polar wander. We propose that hotspots may come from distinct mantle boundary layers, and that the primary ones trace shifts in quadrupolar convection in the lower mantle.

Simultaneous generation of hotspots and superswells by convection in a heterogeneous planetary mantle

Mounting evidence indicates that the Earths mantle is chemically heterogeneous. To understand the forms that convection might take in such a mantle, I have conducted laboratory experiments on thermochemical convection in a fluid with stratified density and viscosity. For intermediate density contrasts, a ‘doming’ regime of convection is observed, in which hot domes oscillate vertically through the whole layer while thin tubular plumes rise from their upper surfaces. These plumes could be responsible for the ‘hot spots’ and the domes themselves for the ‘superwells’ observed at the Earths surface. In the Earths mantle, the doming regime should occur for density contrasts less than about 1%. Moreover, quantitative scaling laws derived from the experiments show that the mantle might have evolved from strictly stratified convection 4 Gyr ago to doming today. Thermochemical convection can thus reconcile the survival of geochemically distinct reservoirs with the small amplitude of present-day density heterogeneities inferred from seismology and mineral physics.

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

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 10 6 and 10 8 and viscosity contrasts are up to 10 6 . 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 k m and ν m 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. Δ T v , 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 T m 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 (2Δ T v ).

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

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.

Heat flow and thickness of the lithosphere in the Canadian Shield

Heat flow and radioactive heat production data were obtained in the Canadian Shield in order to estimate the crustal heat production and the mantle heat flow. Several methods have been used to determine radioactive heat production in the crust. The analysis yields values for the mantle heat flow in the craton that are consistently between 7 and 15 mW m -2 . Assuming that the lithosphere is in thermal equilibrium, we investigate the conditions for small-scale convection to supply the required heat flux through its base. For a given creep raw, the thickness of the lithosphere, the temperature at the base of the lithosphere, and the effective viscosity of the mantle are determined from the value of the mantle heat flow beneath the shield. The viscosity of the mantle depends on the creep mechanism and on the fluid content. Wet diffusion creep implies a viscosity between 10 20 and 10 21 Pa s, corresponding to a mantle temperature of 1620 K at a depth of 250 km. The other creep mechanisms can be ruled out because they imply values for viscosity and temperature inconsistent with geophysical data. For a given creep raw, there is a minimum mantle temperature below which equilibrium cannot be reached. For wet diffusion creep, this minimum mantle temperature (1780 K at 280 km depth) is close to that of the well-mixed (isentropic) oceanic mantle at the same depth. For a thermally stable lithosphere, out model requires the mantle heat flow to be at least 13 mW m -2 and the compositional lithosphere to be less than 240 km.

How to anchor hotspots in a convecting mantle

Laboratory experiments were performed to study the influence of density and viscosity layering on the formation and stability of plumes. Viscosity ratios ranged from 0.1 to 6400 for buoyancy ratios between 0.3 and 20, and Rayleigh numbers between 105 and 2.108. The presence of a chemically stratified boundary layer generates long-lived thermochemical plumes. These plumes first develop from the interface as classical thermal boundary layer instabilities. As they rise, they entrain by viscous coupling a thin film of the other layer and locally deform the interface into cusps. The interfacial topography and the entrainment act to further anchor the plumes, which persist until the chemical stratification disappears through entrainment, even for Rayleigh numbers around 108. The pattern of thermochemical plumes remains the same during an experiment, drifting only slowly through the tank. Scaled to an Earth’s mantle without plate tectonics, our results show that: (1) thermochemical plumes are expected to exist in the mantle, (2) they could easily survive hundreds of millions of years, depending on the size and magnitude of the chemical heterogeneity on which they are anchored, and (3) their drift velocity would be at most 1–2 mm/yr. They would therefore produce long-lived and relatively fixed hotspots on the lithosphere. However, the thermochemical plumes would follow any large scale motion imposed on the chemical layer. Therefore, the chemical heterogeneity acts more as a ‘floating anchor’ than as an absolute one.

Thermal convection in lava lakes

In magma reservoirs, large temperature contrasts imply large variations of viscosity. We determine the characteristics of thermal convection in the laboratory for viscosity ratios of up to 106. In a fluid layer cooled from the top, convection develops below a stagnant lid. Plumes generate temperature fluctuations whose magnitude, θmax, is proportional to the temperature contrast across the unstable region, ΔTe. Scaling analysis and experimental data show that both temperature scales depend solely on the local function describing the variation of viscosity µ at temperatures close to that of the layer interior, Tm, and are equal to: In the Makaopuhi lava lake (Hawaii), temperature fluctuations were recorded below the growing crust. For the viscosity function of the Makaopuhi magma, their magnitude is predicted to be 18°C, in agreement with the observations.

Thermal convection in a heterogeneous mantle

Both seismology and geochemistry show that the Earths mantle is chemically heterogeneous on a wide range of scales. Moreover, its rheology depends strongly on temperature, pressure and chemistry. To interpret the geological data, we need a physical understanding of the forms that convection might take in such a mantle. We have therefore carried out laboratory experiments to characterize the interaction of thermal convection with stratification in viscosity and in density. Depending on the buoyancy ratio B (ratio of the stabilizing chemical density anomaly to the destabilizing thermal density anomaly), two regimes were found: at high B, convection remains stratified and fixed, long-lived thermochemical plumes are generated at the interface, while at low B, hot domes oscillate vertically through the whole tank, while thin tubular plumes can rise from their upper surfaces. Convection acts to destroy the stratification through mechanical entrainment and instabilities. Therefore, both regimes are transient and a given experiment can start in the stratified regime, evolve towards the doming regime, and end in well-mixed classical one-layer convection. Applied to mantle convection, thermochemical convection can therefore explain a number of observations on Earth, such as hot spots, superswells or the survival of several geochemical reservoirs in the mantle. Scaling laws derived from laboratory experiments allow predictions of a number of characteristics of those features, such as their geometry, size, thermal structure, and temporal and chemical evolution. In particular, it is shown that (1) density heterogeneities are an efficient way to anchor plumes, and therefore to create relatively fixed hot spots, (2) pulses of activity with characteristic time-scale of 50–500 Myr can be produced by thermochemical convection in the mantle, (3) because of mixing, no ‘primitive’ reservoir can have survived untouched up to now, and (4) the mantle is evolving through time and its regime has probably changed through geological times. This evolution may reconcile the survival of geochemically distinct reservoirs with the small amplitude of present-day density heterogeneities inferred from seismology and mineral physics.Both seismology and geochemistry show that the Earths mantle is chemically heterogeneous on a wide range of scales. Moreover, its rheology depends strongly on temperature, pressure and chemistry. To interpret the geological data, we need a physical understanding of the forms that convection might take in such a mantle. We have therefore carried out laboratory experiments to characterize the interaction of thermal convection with stratification in viscosity and in density. Depending on the buoyancy ratio B (ratio of the stabilizing chemical density anomaly to the destabilizing thermal density anomaly), two regimes were found: at high B, convection remains stratified and fixed, long-lived thermochemical plumes are generated at the interface, while at low B, hot domes oscillate vertically through the whole tank, while thin tubular plumes can rise from their upper surfaces. Convection acts to destroy the stratification through mechanical entrainment and instabilities. Therefore, both regimes are transient and a given experiment can start in the stratified regime, evolve towards the doming regime, and end in well-mixed classical one-layer convection. Applied to mantle convection, thermochemical convection can therefore explain a number of observations on Earth, such as hot spots, superswells or the survival of several geochemical reservoirs in the mantle. Scaling laws derived from laboratory experiments allow predictions of a number of characteristics of those features, such as their geometry, size, thermal structure, and temporal and chemical evolution. In particular, it is shown that (1) density heterogeneities are an efficient way to anchor plumes, and therefore to create relatively fixed hot spots, (2) pulses of activity with characteristic time-scale of 50–500 Myr can be produced by thermochemical convection in the mantle, (3) because of mixing, no ‘primitive’ reservoir can have survived untouched up to now, and (4) the mantle is evolving through time and its regime has probably changed through geological times. This evolution may reconcile the survival of geochemically distinct reservoirs with the small amplitude of present-day density heterogeneities inferred from seismology and mineral physics.

Stability of thermal convection in two superimposed miscible viscous fluids

The stability of two-layer thermal convection in high-Prandtl-number fluids is investigated using laboratory experiments and marginal stability analysis. The two fluids have different densities and viscosities but there is no surface tension and chemical diffusion at the interface is so slow that it is negligible. The density stratification is stable. A wide range of viscosity and layer depth ratios is studied. The onset of convection can be either stationary or oscillatory depending on the buoyancy number B, the ratio of the stabilizing chemical density anomaly to the destabilizing thermal density anomaly: when B is lower than a critical value (a function of the viscosity and layer depth ratios), the oscillatory regime develops, with a deformed interface and convective patterns oscillating over the whole tank depth; when B is larger than this critical value, the stratified regime develops, with a flat interface and layers convecting separately. Experiments agree well with the marginal stability results. At low Rayleigh number, characteristic time and length scales are well-predicted by the linear theory. At higher Rayleigh number, the linear theory still determines which convective regime will start first, using local values of the Rayleigh and buoyancy numbers, and which regime will persist, using global values of these parameters.

Large interface deformation in two-layer thermal convection of miscible viscous fluids

Laboratory experiments have been performed to study two-layer thermal convection with large interface deformations. The two fluids have different densities and viscosities but there is neither surface tension nor chemical diffusion at the interface. The initial density stratification is stable, but can be reversed by thermal effects. Two different mechanisms of interface deformation are described: (i) purely thermal features due to convection inside each layer independently can locally and partially deform the interface, leading to dynamic topography; (ii) when the effective buoyancy number (the ratio of the stabilizing chemical density anomaly to the destabilizing thermal density anomaly) reaches a critical value, a whole-layer regime takes place, where the system is fully destabilized and one of the two layers invades the other one in the form of large domes. Several successive pulsations can be observed provided the viscosity ratio is large enough (i.e. > 5). Typical scales (time, length, temperature excess, velocity) and behaviours (direction of spouting, shapes) are determined for each case. Both features are only transient states: because of stirring, the system systematically evolves towards one-layer Rayleigh-Benard convection