Numerical models of mantle convection with secular cooling |
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| Authors: | Wanda DeLandro-Clarke Gary T Jarvis |
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| Institution: | Centre for Research in Earth and Space Science, York University, 4700 Keele St., North York, Ontario, Canada M3J 1P3;Department of Earth and Atmospheric Science, York University, 4700 Keele St., North York, Ontario, Canada M3J 1P3 |
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| Abstract: | A 2-D time-dependent finite-difference numerical model is used to investigate the thermal character and evolution of a convecting layer which is cooling as it convects. Two basic cooling modes are considered: in the first, both upper and lower boundaries are cooled at the same rate, while maintaining the same temperature difference across the layer; in the second, the lower boundary temperature decreases with time while the upper boundary temperature is fixed at 0°C. The first cooling mode simulates the effects of internal heating while the second simulates planetary cooling as mantle convection extracts heat from, and thereby cools, the Earth's core. The mathematical analogue between the effects of cooling and internal heating is verified for finite-amplitude convection. It is found that after an initial transient period the central core of a steady but vigorous convection cell cools at a constant rate which is governed by the rate of cooling of the boundaries and the viscosity structure of the layer. For upper-mantle models the transient stage lasts for about 30 per cent of the age of the Earth, while for the whole mantle it lasts for longer than the age of the Earth. Consequently, in our models the bulk cooling of the mantle lags behind the cooling of the core-mantle boundary. Models with temperature-dependent viscosity are found to cool in the same manner as models with depth-dependent viscosity; the rate of cooling is controlled primarily by the horizontally averaged variation of viscosity with depth. If the Earth's mantle cools in a similar fashion, secular cooling of the planet may be insensitive to lateral variations of viscosity. |
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| Keywords: | convection core-mantle boundary mantle convection thermal history |
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