Abstract: Predictability of Rayleigh-number and continental-growth evolution of a dynamic model of the Earth's mantle​

U. Walzer and R. Hendel. Predictability of Rayleigh-number and continental-growth evolution of a dynamic model of the Earth's mantle. In S. Wagner, M. Steinmetz, A. Bode, and M. Brehm, editors, High Perf. Comp. Sci. Engng. Garching/Munich 2007, pages 585-600. Berlin, 2009.

Predictability of Rayleigh-Number and Continental-Growth Evolution of a Dynamic Model of the Earth’s Mantle

Uwe Walzer¹ and Roland Hendel¹

Abstract

We compute a model of thermal and chemical evolution of the Earth’s mantle by numerically solving the balance equations of mass, momentum, energy, angular momentum and of four sums of the number of atoms of the pairs ²³⁸U–²⁰⁶Pb, ²³⁵U–²⁰⁷Pb, ²³²Th–²⁰⁸Pb, and ⁴⁰K–⁴⁰Ar. We derive marble-cake distributions of the principal geochemical reservoirs and show that these reservoirs can separately exist even in a present-day mantle in spite of 4500 Ma of thermal convection. We arrive at plausible present-day distributions of continents and oceans although we did not prescribe number, size, form, and distribution of continents. The focus of this paper is the question of predictable and stochastic portions of the phenomena. Although the convective flow patterns and the chemical differentiation of oceanic plateaus are coupled, the evolution of time-dependent Rayleigh number, Ra_t, is relatively well predictable and the stochastic parts of the Ra_t(t)-curves are small. Regarding the juvenile growth rates of the total mass of the continents, predictions are possible only in the first epoch of the evolution. Later on, the distribution of the continental growth episodes is increasingly stochastic. Independently of the varying individual runs, our model shows that the total mass of the present-day continents is not generated in a single process at the beginning of the thermal evolution of the Earth but in episodically distributed processes in the course of geological time. This is in accord with observation. Section 4 presents results on scalability and performance.

Key words: Earth, mantle, convection, mantle convection, predictability, Rayleigh number, chemical evolution, geochemical reservoirs, thermal convection, continent, flow patterns, continental growth, thermal evolution, numerical model, scalability, performance, chemical differentiation, Terra, convergence test, CPU-time, yield stress, viscosity.

Citation: Walzer, U. and R. Hendel. Predictability of Rayleigh-number and continental-growth evolution of a dynamic model of the Earth's mantle. In S. Wagner, M. Steinmetz, A. Bode, and M. Brehm, editors, High Perf. Comp. Sci. Engng. Garching/Munich 2007, pages 585-600. Berlin, 2009.
¹Institut f. Geowissenschaften, Friedrich-Schiller-Universität, Burgweg 11, 07749 Jena, Germany.

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