RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 7, ES3001, doi:10.2205/2005ES000179, 2005
[27] Within the framework of the theory of mantle convection and tectonics of lithospheric plates, both assemblage of continents and breakup of supercontinents were accounted for by the nonstationarity of convection. At large Rayleigh numbers, thermal convection is nonstationary, the shape and sizes of cells permanently vary, and mantle flows are reorganized. For this reason, it was believed that two or more continents can randomly converge toward a mantle downwelling, forming a supercontinent that can in turn break up if a large mantle upwelling arise beneath it.
[28] However, numerical modeling showed that the processes of continental drift and formation and breakup of supercontinents are not chaotic but obey laws of the tectonics of floating continents. Continents are coupled with the mantle through nonlinear thermal and mechanical interactions, so that not only the mantle affects continents but also the continents can reorganize mantle flows.
[29] To gain constraints on the coupling between mantle and continents, we examined a
simple 2-D Cartesian model of two continents floating on a highly viscous
mantle. We took the simplest model of the type
h=1023 exp(-4.6 T+0.9 H) Pa s,
in which the viscosity decreases by two orders with increasing temperature
and increases by 2.5 times with increasing pressure. The effective Rayleigh
number was specially taken very small (Ra = 2
10
4 ) to make the convection
intensity low, with the Nusselt number Nu = 6. Convection in this model is
stationary and laminar, so that no plumes can arise in this model in the absence
of continents.
[30] After the thermal convection in the mantle had attained a steady-state pattern, two freely floating continents were placed on the mantle. They were modeled by two solid floating plates 300 km thick. These plates can be interpreted as incipient primary continents consisting of continental crust coupled with the oldest strong thin continental lithosphere. Numerical solution of equations of mass, heat and momentum transfer in viscous mantle and Euler equations for the solid continents provides a description for the evolution of the mantle-continents system including the origination, growth, and further evolution of the continental lithosphere. The equations of mantle convection and boundary conditions, as well as a method of their solution, are described in Appendix.
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Figure 1 |
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Figure 2 |
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Figure 3 |
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Figure 4 |
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Figure 5 |
[32] Mantle flow velocities are shown in the figures by black arrows whose maximum length corresponds to a value of about 4 cm yr -1 (upon conversion to Ra = 10 6 ). The dimensionless temperature distribution is characterized by various colors. Hot mantle upwellings are shown by red, whereas the cold highly viscous oceanic lithosphere sinking in subduction zones and transformed into cold mantle downwellings is shown by blue. The continents are represented by gray segments. Reddish brown colors the calculated distribution curve of the dimensionless mantle heat flux Nu( x ). The green line is the calculated seafloor topography.
[33] Figure 1 presents the structure of mantle convection calculated at the stage of
assemblage of continents into a supercontinent. At the time moment
t=0, when
the continents were placed into the mantle, convective cells had a regular
symmetric shape. The heat flux is elevated (about 200 mW m-2 after the
conversion to Ra = 5
106 ) above mantle upwellings and reduced above
downwellings. The continents seat on both sides of the middle mantle downwelling
and are not underlain by a continental lithosphere at the initial time moment.
[34] Calculation of the evolution of the mantle-continents system showed that the continents start moving toward the downwelling under the action of tangential viscous forces. By the time moment t = 15 Myr, each continent moved for about 300 km at an average velocity of about 2 cm yr-1. By this time, the continents converged and formed a supercontinent. Since the heat transfer mechanism in the continents is purely conductive, they hinder the removal of heat from the mantle. As seen from Figure 1, the heat flux through the supercontinent (about 30 mW m-2 ) is nearly six times smaller than in ridge zones. The mantle material under the supercontinent is still cold and heavy and continues to descend, compressing the supercontinent.
[35] Further calculation of the mantle convection evolution at the supercontinent stage is illustrated in Figure 2. Due to the heat screening effect, the cold mantle material beneath the supercontinent starts heating and thereby becomes lighter. Approximately after 200 Myr (with other values of parameters, after 400 Myr [Bobrov et al., 1999]), the downwelling beneath the supercontinent gives way to a giant ascending mantle flow withdrawing heat from the mantle base. However, as seen from Figure 2, this hot mantle upwelling increases the heat flux above the supercontinent still insignificantly due to the heat-screening effect of the crust and continental lithosphere.
[36] Figure 3 shows the region under the supercontinent on a larger scale. Isolated floating-up diapirs periodically arise at the center of the wide mantle upwelling; when detached, they are transformed into separate hot spots (thermals). Note once more that, in the absence of continents, plumes cannot arise in this model with a small Rayleigh number (see Animation 1 for more details of plume evolution).
[37] Figure 4 shows the convection structure and the position of the continents at the stage of their divergence after the breakup of the supercontinent. The continents diverge in opposite directions from the central hot mantle flow. Although the mantle beneath the continents is very hot, the heat flux crossing the continents is still small (40-50 mW m-2 ) because the heat from the hot mantle plume did not reach the Earth's surface at this time.
[38] As the continents continue diverging, the hot mantle upwelling is enhanced. Accordingly, the heat flux from the mantle also increases, attaining maximum values of more than 200 mW m-2, but does not exceed 20-30 mW m-2 above the continents because they hamper the heat transfer.
[39] At the time moment t = 290 Myr, a structure of the Atlantic Ocean type arises between the continents. A mid-ocean ridge with a high heat flux is observed in its axial zone. The colder region of the mantle (corresponding to the oceanic lithosphere) thickens away from the ridge. On the other side of the continents, there arose a structure of the Pacific Ocean type along with subduction zones, where the oceanic lithosphere plunges into the mantle beneath the continents.
[40] The structure that arose by the time moment t = 340 Myr is hypothetically conceivable as a future Atlantic Ocean when its greatly extended oceanic lithospheric plates will start sinking at the margins of Europe and North America. From this time, the Atlantic Ocean can be similar to the present Pacific Ocean (see Animation 2 for more details).
[41] The calculated models are a result of numerical experiments based on the solution of classical differential equations of energy, mass, and momentum transfer. These experiments show that, during convection, two plates floating over a heated viscous fluid must periodically converge above a descending flow, after which they must inevitably diverge. The time between their assemblages depends on the viscosity and temperature of the fluid. Taking into account results of similar 3-D model calculations presented in [Trubitsyn and Rykov, 1995] and converting them to mantle parameters, it may be supposed that the time intervals between formations of supercontinents amounted to 0.5-1.0 Gyr.
Citation: 2005), Evolution of mantle plumes and uplift of continents during the Pangea breakup, Russ. J. Earth Sci., 7, ES3001, doi:10.2205/2005ES000179.
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