Dynamics and internal structure of a lower mantle plume conduit

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Abstract

Geochemical studies, including those made possible by the Hawaiian Scientific Drilling Project, have revealed the chemically and isotopically heterogeneous nature of hotspot lavas, yet their interpretation is highly controversial and there is little agreement as to how geochemical heterogeneities might be spatially arranged within the plume conduit. To address this issue we conduct high resolution numerical simulations of an axisymmetric purely thermal plume, focusing on the lower mantle part of the conduit and on the thermal boundary layer (TBL) feeding the plume. We explore the relation between length-scales of heterogeneities across the source region and the length- and time-scales of geochemical variations in the plume conduit. The vertical velocity inside the conduit decreases exponentially with the square of radial distance generating high strain rates (order 10 13–10 14 s 1) that modify the shape of upwelling heterogeneities into elongated and narrow filaments. Therefore, the preservation of ‘blob-like’ heterogeneities (i.e., with a 1:1 aspect ratio in a vertical section) is quite unlikely, even in the central part of the plume. For example, initial lenses of size 100 × 10 km in the TBL are stretched into filaments 500–1000 km long. These filaments constitute ‘long-lived’ structures in a rising plume, and their geochemical fingerprints may be registered at a given radial distance for several millions of years. We also consider an idealized heterogeneous architecture inside the TBL, consisting of ‘trains’ of small scale lenses. When such trains upwell in the conduit, they form high radial geochemical gradients. Their ‘geochemical record’, registered over time at a given depth and radial distance, will fluctuate over time, with shorter period and a larger amplitude at the conduit center than at its periphery. Finally, we demonstrate that material existing ‘side by side’ in the conduit originated from regions in the TBL that are separated by distances of several hundred kilometers. This implies that vigorous plumes are able to sample, and to bring side by side, very distant portions of their source region. Our results provide a fluid dynamically consistent framework to discuss the main aspects of the different (and to some extent mutually exclusive) models of conduit structure used to interpret the geochemical observations of the Hawaiian lavas.

Introduction

Geochemical studies of Hawaiian basalts have yielded a wealth of data relevant to the understanding of the chemical and isotopic internal structure of mantle plumes. However, the interpretation of these data has remained highly controversial, partly because there are significant uncertainties as to how the volcanic plumbing system samples the underlying plume, but also because there is little agreement as to how the existing geochemical heterogeneities might be spatially arranged within the plume conduit. The pioneering model by Hauri et al. (1994), suggested a concentrically zoned plume conduit, whereby geochemical variations occur only in the radial direction, due to entrainment of surrounding mantle. Entrainment is governed by thermal diffusion and is expected to decrease with increasing plume flux (Hauri et al., 1994). In spite of the high buoyancy flux of the Hawaiian plume (Sleep, 1990) the concentric model has been extensively invoked to explain the time and space variability of isotope ratios e.g., (DePaolo and Stolper, 1996, Hauri et al., 1996, Lassiter et al., 1996). However, recent data from the Hawaiian Scientific Drilling Project HSDR-2, have shown spatial and temporal variations for Pb, Nd, Hf, and Sr isotope ratios (see DePaolo et al., 2001, Blichert-Toft et al., 2003, Eisele et al., 2003, Abouchami et al., 2005, Bryce et al., 2005) and references therein) that are inconsistent with concentric zoning and have prompted the suggestion of new conceptual models.

Presenting a contrasting view of the internal plume structure, Blichert-Toft et al. (2003) propose a plume structure that minimizes radial variations across the conduit by assuming a ‘plug-flow’, whereby the vertical velocity remains nearly constant across the main part of the conduit and decreases sharply only at its periphery. The ‘plug-flow’ velocity profile contrasts with the exponentially varying velocity profile derived analytically by Olson et al. (1993). According to Blichert-Toft et al. (2003) the geochemical cross section of the plume does not need to be time invariant, so that the conduit structure may be similar to a stack of nearly horizontal thin ‘layers’ with distinct isotope ratios.

In yet another interpretation (Eisele et al., 2003, Abouchami et al., 2005) the conduit internal structure is similar to a bundle of vertically elongated filaments, successively sampled by different volcanoes as the Pacific plate moves over the Hawaiian plume. The underlying physical process is stretching of deep heterogeneities due to velocity gradients within the plume conduit.

The above interpretations are purely based on geochemical observations and there is a clear need to investigate the internal structure of a plume conduit from a fluid dynamics perspective. In this paper we use numerical simulations of a thermal plume to address some fluid dynamics questions expected to be relevant for the geochemical interpretation of internal plume structure. First, what is the relation between length-scales of heterogeneities across the source region (assumed to be the D″ layer overlying the core–mantle boundary) and length- and time-scales of geochemical variations once heterogeneities are upwelling in the plume conduit? Second, deep heterogeneities may be thought of as isolated finite-size volumes, or they may be distributed in space so as to form an internal architecture in the D″ region. In this case, what would be the internal structure of a plume conduit fed by such a complex source region? Third, are there fundamental differences between the central and the peripheral zones of the plume conduit, for example due to different deformations undergone during upwelling and/or different parts of the source region being sampled? Finally, which aspects of the three different (and to some extent mutually exclusive) models of conduit structure presented above are consistent with fluid dynamics constraints?

To our knowledge, previous fluid dynamics studies have not explored the relation between finite-size heterogeneities in the thermal boundary layer (TBL) and the conduit internal structure. Although it is beyond the scope of our paper to review the important contributions of laboratory experiments and numerical models for the understanding of mantle plumes, we note that early laboratory experiments, for example by Griffiths and Campbell (1990), focused on the plume head rather than on the long lived conduit. Moreover, laboratory experiments have rigid bottom boundary conditions and the hot plume is often injected in the tank, thereby precluding any investigation of the dynamics and internal deformations in the basal TBL. More recent experiments by Kerr and Mériaux (2004) on plumes upwelling in a mantle wind generated by surface plate motion, concluded that the Hawaiian plume conduit should be zoned azimuthally, rather than concentrically. However, Kerr and Mériaux (2004) did not consider the deformations of finite-size heterogeneities, nor did they quantify strain rates across the conduit and the TBL.

Our work is based on a purely thermal flow within an idealized TBL and the associated plume conduit. Certainly, the D″ region is more complex than a thermal boundary layer (see for example Jellinek and Manga, 2004, Garnero and McNamara, 2008, and references therein), and our model does not include most of the recent findings, namely the post-perovskite phase transition (Murakami et al., 2004) and the existence of chemical heterogeneities in the deep mantle. While the role of the post-perovskite on mantle plumes is still a matter of debate, it is now clear that chemically denser material plays an important role on plumes shape and dynamics (Tackley, 1998, Davaille, 1999, Farnetani and Samuel, 2005), composition (Christensen and Hofmann, 1994, Samuel and Farnetani, 2003) and excess temperature (Farnetani, 1997). We are aware that considering the D″ region as a purely thermal boundary layer is a gross simplification; nevertheless, from a modeling stand point, we consider it important and instructive to start with the most basic fluid flow.

It is also difficult to characterize the geochemical fingerprint of the D″ region. The base of the Earth's mantle is likely to be a slab ‘graveyard’. In such a case, denser subducted crust may segregate and evolve geochemically (Christensen and Hofmann, 1994) before being recycled in mantle plumes (Hofmann and White, 1982). But the D″ region, or parts of it, could also host a ‘hidden reservoir’, with a distinct geochemical composition, remnant from the early differentiation of the Earth's mantle (Boyet and Carlson, 2005, Tolstikhin and Hofmann, 2005). Deliberately, we do not attempt to reproduce this complex geochemistry and geochemical evolution over time. Instead, we conduct a ‘thought experiment’ to investigate the relation between a hypothetically heterogeneous D″ and the internal structure of a plume conduit.

Finally, we had to restrict our modeling to a few examples of kilometer scale geochemical heterogeneities with simple shapes and basic spatial orientations, which are certainly poor representations of the great variety created by mantle stirring. As reviewed by Hofmann (2003) the spatial scale of heterogeneities may vary from 102–104 km, to the decimeter scale (Allègre and Turcotte, 1986) and less. On the other hand, the kilometer-scale explored here is likely to be particularly relevant to mantle plumes, particularly in view of the rapid fluctuations in isotopic composition observed in the stratigraphic record of the Hawaiian Scientific Drilling Project (Eisele et al., 2003).

Our high resolution numerical model allows us to calculate deformations in a plume conduit with a detail that is not achieved in global mantle mixing models. Although such models have improved our understanding of convective stirring (see for example Kellogg, 1992, Davies, 2002, van Keken et al., 2003, Tackley, 2007, and references therein), it is important to focus on deformations inside hot, low viscosity and fast upwelling narrow plumes that are likely to represent unique places in the lower mantle where strain rates are particularly high and the associated stretching is more rapid and intense than elsewhere in the lower mantle.

This paper focuses on the basal thermal boundary layer feeding the plume and on the lower mantle part of the conduit, while, in a companion paper (in prep.) we model the dynamics of an upper mantle conduit sheared by a fast moving plate, allowing us to investigate how volcanoes sample a spatially heterogeneous plume conduit.

Lastly, we point out that although our results are used to elucidate the internal structure of the Hawaiian conduit, they may be of interest to other plumes, for example Galápagos, where isotope and incompatible element ratios have a complex spatial distribution, namely a horseshoe pattern with enriched signatures around a depleted center (White et al., 1993, Harpp and White, 2001). Interestingly, the observed asymmetrical spatial zonation of the Galápagos hotspot has persisted for several millions of years (Hoernle et al., 2000), suggesting the involvement of large scale heterogeneities in the source region feeding the plume.

Section snippets

Numerical model

We use the two dimensional code ConmanCYL (Farnetani, 1997, King et al., 1990) in cylindrical geometry to solve the equations of conservation of mass, conservation of momentum and conservation of energy for an incompressible viscous fluid at infinite Prandtl number. The size of the model domain is 1500 × 2890 km in the radial and vertical directions, respectively. The element size is 4 × 4 km in the regions of interest (i.e., the TBL and the plume conduit), elsewhere in the lower mantle the element

Results

Starting from the initial condition described above we run the calculation until the transient plume head reaches the base of the lithosphere and the velocity field approaches steady state. Fig. 1a (solid line) shows the vertical velocity component vz as a function of radial distance r across the plume conduit at 2000 km depth: at the axis vaxisz = 50 cm/yr, at r = 38 km vz = vaxisz/2 and at r = 70 km vz = vaxisz / 10. The radial dependence of vz is quite invariant throughout the height of the plume and it

Comparison with previous models of conduit structure and conclusion

The first conceptual model of conduit structure was suggested nearly fifteen years ago and is known as the ‘concentric zoning’ (Hauri et al., 1994, DePaolo and Stolper, 1996) whereby the plume center samples the deepest part of the TBL, while the conduit periphery either samples the upper part of the TBL (Farnetani et al., 2002, Bryce et al., 2005) or, in case of entrainment, it samples also the surrounding mantle (Hauri et al., 1996). Our simulations confirm one basic idea of the concentric

Acknowledgements

We thank Bill White, Ross Kerr and an anonymous reviewer for their constructive and useful reviews. Erik Hauri provided thorough comments on an earlier version of the manuscript. CGF thanks Bernard Legras for discussions of the Supplementary Material and Claude Jaupart for support. We also wish to thank Rick Carlson for his editorial handling. IPGP Contribution No. 2489; LDEO Contribution No. 7247.

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