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

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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.