The role of convective mixing in degassing the Earth's mantle

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Abstract

The chemical evolution of the mantle depends on the way rocks are processed at the surface of the Earth and on the efficiency of convective mixing. In order to quantify how mixing and processing depend on convection parameters (Rayleigh number, heating mode and viscosity stratification), I conducted an extensive set of simple 2D convection simulations with passive tracers and compute (a) bulk Lagrangian strain rates to evaluate mixing efficiency and (b) processing histories. At high Rayleigh number, the strain rate is only a function of the velocity of the flow, whatever the heating mode or viscosity stratification. This is not the case in low Rayleigh number experiments with basal heating where a transition regime is observed with inefficient mixing though chaotic. The simulations show that the processing efficiency depends a lot on the heating mode: the probability of sampling primordial rocks is larger with internal heating than with basal heating. Scaling laws are proposed to parameterize mantle processing histories and it is predicted that in a 300 K hotter Earth, convection can account for the early degassing of the mantle (more than 90% in less than 100 Myr).

Introduction

In the search of a holistic view of the chemical evolution of the Earth's mantle, many models have been proposed with the goal of matching geophysical and geochemical observations [1], [2]. On one hand geophysical models can explain thermal histories but do not explain fully the complexity of geochemical observations [3], [4], [5]. On the other hand, geochemical models are built to fit the chemical data [6], [7], [8] but contradict the physics of the mantle [9], [10]. Recently, sophisticated modeling of the chemical evolution of the mantle incorporating plate-like behavior got closer to the achievement of computing accurate and Earth-like thermo-chemical simulations [11]. Though, computing a realistic mantle evolution from first principles involves a complexity beyond our present day capabilities.

The two major links between the physics of convection and the chemistry of mantle rocks are the processes of mixing and extraction at mid ocean ridges. Mechanical mixing studies tend to show that because mixing is chaotic, it is doubtful to predict the mixing properties of a flow from simple flow parameters [12], [13], [14], [15]. Especially, the deformation of a heterogeneity introduced in a flow depends drastically on details of the velocity field. However, most of these works employ analytic Stokes flows or imposed surface velocities neglecting the role of self-organization of convection, and focus on the spatial mixing pattern instead of average mixing behavior. Hence, the question of a relationship between convection parameters and average mixing efficiency remains.

Processing at mid ocean ridges has been treated mostly in studies of isotopic evolution of the mantle [11], [16]. It has been shown that homogeneous convection rapidly processes the whole mantle domain and that isolation of pristine regions is not possible unless models involve intrinsic density and viscosity differences in the medium [2]. Although, quantifications of how convection parameters influence processing still have to be done. Though unsatisfactory [19], box models (where processing decays as a function of the residence time) represent the most common analytic tool to perform chemical evolution simulations [17], [18].

The aim of the present paper is to extract quantitative relationships between physical parameters of convection (Rayleigh number, heating mode, viscosity stratifications), mixing and processing through an extensive set of 2D numerical simulations of free homogeneous convection. These calculations are further motivated by two other objectives: building parameterized models more physically sounded than box-models and contributing to constrain the history of mantle degassing.

The numerical setup is first described introducing the primordial variables used to measure mixing and processing. Then the roles of the Rayleigh number, heating mode and viscosity stratification are detailed. Finally, the relevance of the results of the 2D simulations and the consequences of this study for the Earth's mantle are discussed.

Section snippets

Experimental setup

To explore relationships between convection, mixing and chemical histories, I propose an experimental setup based on fluid mechanics, physics of mixing and analytical processing models.

Mixing, heating mode and viscosity stratification

In this section, the numerical experiments show that there is a relationship between ɛ˙ and Ra, that mixing in internally heated convection differs from that of basally heated convection, and the viscosity stratification does not impede mixing.

Processing, heating mode and viscosity stratification

Numerical experiments show that heating mode greatly influences processing contrarily to viscosity stratification. In the numerical experiments where mixing is regular, linear processing is observed with Em close to 0.25. In steady flows, only the streamlines crossing the processing boundary can provide particles, the rest leaving unsampled. In this section, I discuss cases corresponding to random sampling only. They correspond to simulations involving chaotic mixing. The maximum processed

Geodynamic interpretations

The simulations provide scaling laws that can be used to parameterize the processing and degassing history of the Earth's mantle.

Conclusions

In the present study, I show that bulk mixing and processing in the mantle can be constrained by the parameters of convection. At high Ra, mixing is chaotic and the mean Lagrangian strain rate scales with the velocity. The heating mode plays a fundamental role in the mixing behavior:

  • (a)

    mixing is inefficient at low Ra (ɛ˙Ra1.3) with bottom heating,

  • (b)

    mixing efficiency does not depend on the viscosity stratification and is only a function of the velocity of the flow,

  • (c)

    mixing is always efficient with

Acknowledgements

I would like to thank Yanick Ricard and Marc Monnereau for their comments and their support. Constructive comments from an anonymous reviewer helped improve the manuscript. This paper benefited from the editorship of Rob van der Hilst. This work was sponsored by the DyETI program of CNRS-INSU.

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