Hard turbulent thermal convection and thermal evolution of the mantle

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Abstract
This article summarizes the results of hard turbulent convection obtained in laboratory experiments and numerical simulations. Its applications to mantle convection are illustrated by two‐dimensional numerical solutions to (1) Newtonian, (2) non‐Newtonian convection and (3) Newtonian convection with multiple phase transitions. In Newtonian mantle convection the transition from soft to hard turbulence is marked by the appearance of disconnected plumes. Spectral analysis of the time series of the Nusselt number reveals the presence of a spectral scaling subrange for hard turbulence but not for soft turbulence. In hard turbulence there is correspondence between the spectra in frequency and wavenumber domains. The slope of the seismic wave spectra measured from seismology suggests that the mantle convection today is strongly time‐dependent. The transition to hard‐turbulence takes place at much lower Nusselt numbers for non‐Newtonian than for Newtonian rheology. For the mantle this would have important ramifications. Non‐Newtonian plumes behave quite differently from Newtonian ones in that large curvatures are developed in their trajectories in the hard turbulent regime. Mantle convection with phase transitions tends to become more layered with increasing Rayleigh numbers. The style of mantle convection might have changed from a layered to a more whole mantle type of flow with time. Catastrophic overturns associated with strong gravitational instabilities in the transition zone could be responsible for superplume events.