Impact of the Rayleigh number and endothermic phase transition on the time behaviour of mantle avalanches

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There has been a long history of studying the endothermic phase change at a depth of 660km in the Earth's mantle. The goal of the present study is to determine the transition between one-layered convection and two-layered circulation and to analyze the dynamics of mantle avalanches using simple two-dimensional numerical models. A series of numerical calculations have been investigated using different Rayleigh numbers (Ra) and Clapeyron slopes (γd). It has been established that the Rayleigh number effectively influences the dynamics of the phase transition. At higher Rayleigh numbers the hindering effect is stronger; at γd<0 mantle convection is shifted from one-layered towards a partially layered flow system. From calculating the vertical mass flux at 660km and analysing its time series three types of mantle flow were found. The first type is whole mantle convection (one-layered), namely below Ra=105 and for γd=−3, −4.5, −6, −9MPa/K. The second type is an intermittently layered mantle convection, where the convection is mainly layered but there is a significant, episodically huge mass transfer between the two layers, i.e. above Ra=5×105 and for γd=−3, −4.5, −6MPa/K. The third type covers isolated upper and lower mantle convection at γd=−9MPa/K and from Ra=105, within which range all of the simulations resulted in two-layered convection. Systematic investigation has been carried out to map the region in the second group where avalanche events can appear. Mantle avalanches have been detected in 12 models from Ra=5×105 to Ra=107 and at γd=−3, −4.5, −6MPa/K. As a result of a Fourier analysis the characteristic time periods of mantle avalanches have been calculated. Analysing the amplitude spectrum of the vertical mass flux at a depth of 660km two specific time periods were determined. The larger one, at about 580Myr, may correspond to the large mantle overturns. The shorter period represents smaller, more frequent mantle avalanches. Studying the influence of the Rayleigh number and the Clapeyron slopes systematically, it has been shown that the characteristic time period of these smaller avalanches depends on Ra, but is independent of γd. As Ra increases the time period decreases; the relationship can be well described with a power function. The characteristic time period of small avalanches for mantle-like parameters (Ra∼107, γd=−3MPa/K) is about 80–150Myr, which can be compared to the average time period of episodic flood basalt activity.