Michael Le Bars

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 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.

Fluid flows in a librating cylinder

The flow in a cylinder driven by time-harmonic oscillations of the rotation rate, called longitudinal librations, is investigated. Using a theoretical approach and axisymmetric numerical simulations, we study two distinct phenomena appearing in this librating flow. First, we investigate the occurrence of a centrifugal instability near the oscillating boundary, leading to the so-called Taylor-Gortler vortices. A viscous stability criterion is derived and compared to numerical results obtained for various libration frequencies and Ekman numbers. The strongly nonlinear regime well above the instability threshold is also documented. We show that a new mechanism of spontaneous generation of inertial waves in the bulk could exist when the sidewall boundary layer becomes turbulent. Then, we analyse the librating flow below the instability threshold and characterize the mean zonal flow correction induced by the nonlinear interaction of the boundary layer flow with itself. In the frequency regime where inertial mo...

Coriolis effects on the elliptical instability in cylindrical and spherical rotating containers

The effects of Coriolis force on the elliptical instability are studied experimentally in cylindrical and spherical rotating containers embarked on a table rotating at a fixed rate

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

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Elliptical instability in hot Jupiter systems

. For a given set-up, changing the ratio

The universal aspect ratio of vortices in rotating stratified flows: experiments and observations

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Spontaneous generation of inertial waves from boundary turbulence in a librating sphere

of global rotation

Finite-size effects in parametric subharmonic instability

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