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Slab-parallel advection versus Rayleigh-Taylor instabilities in melt-rich layers in subduction zones: A criticality analysis

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Highlights

  • In subduction zones, Rayleigh-Taylor instability (RTI) and slab-parallel advection control the flows in melt-rich layers.

  • Slab-dip angle (α) is found to be the crucial factor to determine these two competing mechanisms.

  • Laboratory experiments and numerical simulations show a RTI to advection transition at a critical α between 20° and 30°.

  • Linear stability analysis constrains the RTI growth at α < 28°.

  • The competing RTI and advection driven flows decide distributed versus localized arc volcanoes in subduction zones.

Abstract

We show slab-parallel advection and Rayleigh-Taylor instability (RTI) as two competing gravity-driven flow mechanisms in the melt-rich layer atop a subducting slab. Scaled laboratory model results, supported by CFD simulations, indicate a transition of the RTI to advection mechanism at a threshold slab-dip angle (α) between 20° and 30°. The advection mechanism results in updip flow, forming a single plume at the upper edge of the melt-rich layer. Based on lubrication approximation, we present an analytical solution of the linear stability problem to perform a criticality analysis of α for the transition between RTI and advection, as observed in the experiments. The solution indicates this transition to occur at α = 28°, in favorable agreement with the experimental values. The article finally highlights the implications of this criticality analysis in interpreting the spatial distributions of subduction volcanism.

Introduction

Rayleigh-Taylor instability (RTI) plays a critical role in driving planetary processes on a wide spectrum, ranging from the core-mantle segregation and thermal plume generation to salt dome formation in sedimentary basins. RTI studies in the geological perspective focused mainly upon the mechanics of gravity instabilities in horizontally layered settings (Ramberg, 1968, Ramberg, 1972; Whitehead, 1986; Wilcock and Whitehead, 1991; Houseman and Molnar, 1997; Miller and Behn, 2012; Schmalholz and Schmid, 2012; Turcotte and Schubert, 2014; Fernandez and Kaus, 2015). However, in non-horizontal layered systems, the inherent inclinations of the layers become an added factor to influence the RTIs (Lister et al., 2011; Rohlfs et al., 2017; El Jaouahiry and Aniss, 2020). Some experimental findings suggest that updip advection of the buoyant materials can greatly influence the growth of gravitational instabilities in a dipping buoyant layer (Lin and Kondic, 2010; Lin et al., 2012; Dutta et al., 2016). Understanding the role of such layer-parallel advection in the RTI growth has many implications in interpreting gravity-driven structures in various geological settings, such as the development of salt domes on dipping source layers. Recent studies have shown the origin of cold plumes in subduction zones as a consequence of the RTIs in melt-rich zones resting above the inclined subducting slabs (Gerya and Yuen, 2003; Codillo et al., 2018). In such dipping slabs, the layer parallel advection makes the material transport dynamics quite complex, and it cannot be fully explored within a framework of the RTI mechanics for horizontal density stratification. Previous studies suggest that the RTI patterns on inclined buoyant layers are markedly different from those reported for horizontal systems (Lin et al., 2012; Brun et al., 2015; Dutta et al., 2016; Gallaire and Brun, 2017). Unlike axisymmetric gravity structures in horizontal settings, the RTIs patterns show their directional growth in melt-rich layers on dipping slabs. These patterns have been investigated primarily as a function of viscosity ratio of the melt-rich layer and the overlying mantle wedge (Zhu et al., 2009). However, the effects of varying slab-dips on the growth of cold plumes are yet to be fully explored. The slab-dip is expected to largely increase the buoyancy-driven advection of melt-rich materials in the updip direction. This phenomenon is accounted for various hydrodynamic problems, e.g., dripping of water drops down a sloping glass plate (Brun et al., 2015).

In this study, we treat RTI and slab-parallel advection as two competing mechanisms to control the gravity-driven flow in the melt-rich layer above a subducting slab. The two processes are first tested in laboratory-scale experiments and real scale numerical simulations, which show a transition of the RTI to updip advection as the slab-dip angle exceeds a threshold value. Using lubrication approximations (Maiti and Mandal, 2020), a theory is developed to find a dispersion relation for the wave instability in a buoyant layer, and perform a criticality analysis for the RTI/advection transition. Finally, we discuss the implications of this criticality analysis in interpreting contrasting volcano distribution patterns observed in natural subduction zones.

Section snippets

Analogue experiments

We investigated the RTI/ advection transition in scaled laboratory models for both R > 1 and R < 1, where R is the viscosity ratio between the overburden and the buoyant layer. For R > 1, the experimental setup consisted of a glass box (60 cm × 30 cm × 30 cm), and a rectangular wooden plate (60 cm × 30 cm × 5 cm), placed in a slanted position to introduce the desired slab-dip angle (α). Two immiscible fluids were used: hydraulic oil (ρs = 970 kg/m3, μs = 10 Pa s) and semi-transparent glue (ρo

Theory

We adopt a linear stability approach to develop a theory in predicting the critical slab-dip angle (α*) for the RTI/slab-parallel advection transition. Consider a buoyant layer (density: ρ1) of uniform thickness (ho) on a rigid slab with an inclination of α, placed beneath a denser fluid layer of height h2 (density: ρ2) (Fig. 3a). We choose a Cartesian space, xz with the x-axis at the base of the buoyant layer. The system is subject to the acceleration to gravity g in the vertical direction. In

Geological implications

The criticality analysis presented in this article indicates that the RTIs in a buoyant layer can occur only when its inclination is less than ~28°. Inclinations exceeding this threshold value replace the RTI mechanism with a slab-parallel advection. This theoretical prediction applies well to our experimental observation as well as numerical simulations (Fig. 1, Fig. 2). We will now explore how far this criticality analysis can be extended to natural subduction zones.

We choose the Central

Conclusions

  • 1)

    In subduction zones, the slab-dip (α) is found to be the key factor to modulate the two competing mechanisms: slab-parallel advection and Rayleigh-Taylor instability (RTI) in the melt-rich layers resting upon the subducting slabs. A transition from RTI to advection mechanism occurs as α exceeds a critical value.

  • 2)

    The conventional linear stability analysis indicates that the RTI develops with a minimum dominant wavelength (λd) in horizontal layer (i.e., α = 0°). λd increases with increasing α.

CRediT authorship contribution statement

Dip Ghosh:Conceptualization, Formal analysis, Investigation, Methodology, Resources, Validation, Visualization, Writing - original draft, Writing - review & editing.Giridas Maiti:Methodology, Software, Investigation, Visualization.Nibir Mandal:Conceptualization, Supervision, Methodology, Resources, Writing - original draft, Writing - review & editing, Funding acquisition.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

We thank two anonymous reviewers and Editor, Prof. M. Jellinek for their insightful comments and suggestions for improvement of the manuscript. This work was supported by the Science and Engineering Research Board (SERB), India through the J. C. Bose Fellowship (SR/S2/JCB-36/2012) to NM. DG and GM gratefully acknowledge the UGC and the CSIR, India, respectively for awarding them senior research fellowships.

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