Cold Plumes Initiated by Rayleigh-Taylor Instabilities in Subduction Zones, and Their Characteristic Volcanic Distributions: The Role of Slab Dip

Abstract

Dehydration melting in subduction zones often produces cold plumes, initiated by Rayleigh-Taylor instabilities in the buoyant partially molten zones lying above the dipping subducting slabs. We use scaled laboratory experiments to demonstrate how the slab dip (α) can control the evolution of such plumes. For α > 0°, Rayleigh-Taylor instabilities evolve as two orthogonal waves, one trench perpendicular with wavelength λ_L and the other one trench parallel with wavelength λ_T (λ_T > λ_L). We show that two competing processes, (1) λ_L-controlled updip advection of partially molten materials and (2) λ_T/λ_L interference, determine the modes of plume growth. The λ_T/λ_L interference gives rise to an areal distribution of plumes (Mode 1), whereas advection leads to a linear distribution of plumes (Mode 2) at the upper fringe of the partially molten layer. The λ_T wave instabilities do not grow when α exceeds a threshold value (α* = 30°). For α > α*, λ_L-driven advection takes the control to produce exclusively Mode 2 plumes. We performed a series of 2-D and 3-D computational fluid dynamics simulations to test the criticality of slab dip in switching the Mode 1 to Mode 2 transition at α^*. We discuss the effects of viscosity ratio (R) and the density contrast (Δρ) between the source layers and ambient mantle, source layer thickness (T_s), and slab velocity (U_s) on the development of cold plumes. Finally, we discuss the areal versus linear distributions of volcanoes from natural subduction zones as possible examples of Mode 1 versus Mode 2 plume products.

Key Points

• Cold plumes are formed by two sets of Rayleigh-Taylor instability waves: λ_L and λ_T along and across the slab dip
• The λ_T interference and λ_L-controlled updip partial melt advection are the key processes to decide distributed versus localized plume growth
• Steepening slab dip leads to a transition from distributed to localized plume development, as manifested in contrasting arc volcanisms

1 Introduction

Understanding the underlying mechanisms of subduction-driven arc volcanism has recently set a new milestone in geodynamic modeling with a multidisciplinary approach (Grove et al., 2012; Ito & Stern, 1986; Perrin et al., 2018). Natural subduction zones show broadly two types of volcano distributions. One is characterized by approximately regularly spaced volcanoes along a trench parallel linear zone (called linear distribution pattern hereafter), such as the Sumatra and the Caribbean subduction zones. The other is characterized by sporadic distribution of arc volcanoes both parallel and perpendicular to the trench (called areal distribution pattern), such as the Mexican and the South American subduction zones. The linear distribution pattern forms a laterally persistent narrow belt (~10 km wide; Marsh, 1979), also referred to as volcanic front, located at a specific horizontal distance perpendicular to the trench line, corresponding to a vertical depth of ~110 km to the dipping slab boundary (Syracuse & Abers, 2006). A volcanic front displays a regular spacing (30 to 70 km) of the volcanic centers arranged parallel to the trench (Andikagumi et al., 2020; Drake, 1976; Marsh & Carmichael, 1974; Tamura et al., 2002; Vogt, 1974). Despite remarkable progress in subduction zone modeling in recent years (Horiuchi & Iwamori, 2016; Wang et al., 2019; Wilson et al., 2014), the variables that control the locations of arc volcanoes and their spatiotemporal distributions in the overriding plate remain a challenging topic of research in the subduction geodynamics community (Grove et al., 2009, 2012).

It is now widely accepted that dehydration slab melting is the key process to drive arc volcanisms in subduction zones. Subducting slabs undergo dehydration reactions, releasing fluids into the hot mantle wedge (Figure 1a), which in turn causes partial melting by lowering the solidus temperature of rocks in the overlying mantle wedge (Arcay et al., 2005; Davies & Stevenson, 1992; Fumagalli & Poli, 2005; Grove & Till, 2019; Tatsumi, 1989). Stability field of chlorite, which can accommodate as much as ~13 wt% H₂O in its structure, has been used to predict the depth of such dehydration melting in the peridotitic mantle wedge (Till et al., 2012; Zheng et al., 2016). Fertile peridotite with high Al₂O₃ content can host 6 to 7 wt% chlorite that equates to 2 wt% bulk H₂O at the P-T condition of the vapor-saturated peridotite solidus. Petrological calculations suggest chlorite breaks down at depths, corresponding to pressures and temperatures of 2 to 3.6 GPa and 800°C to 860°C, respectively, implying that dehydration melting occurs on the upper slab surface beginning at a depth of 70 km and extending to a depth of 200 km (Bose & Ganguly, 1995; Grove & Till, 2019; Grove et al., 2009; Iwamori, 1998). A number of previous studies have shown that partially molten zones formed by dehydration melting can be 2 to 20 km thick, depending upon the thermal structure of the subduction zone, and the depth and the degree of dehydration melting above the dipping slab (Gerya & Yuen, 2003; Grove et al., 2006, 2009; Marsh, 1979). In some cases, they may incorporate materials derived from serpentinized subduction channel and subducted crustal sediments, as reported from the recycled sediment signatures in arc volcanoes (Marschall & Schumacher, 2012; Zhang et al., 2020).

Figure 1

(a) A 2-D cartoon presentation of cold plume formation from a partially molten layer above the dipping slab in a subduction setting. (b) Two principal modes of evolution of 3-D RTI structures (sketches derived from experiments). Mode 1: spatially distributed dome formation by the interference of longitudinal (λ_L) and transverse (λ_T) instability waves; Mode 2: instability dominated by λ_L waves, which focus updip material advection to localize an array of plumes at the upper edge of the source layer (α: slab dip). The three stages are classified based on normalized experimental runtime t* = t/t_T (t_T is the total runtime; new instabilities almost ceased to occur in the source layer after t_T); Stage I: t* = 0–0.2, Stage II: t* = 0.2–0.6, and Stage III: t* > 0.6.

The extent and minimum depth of dehydration melting in the wedge above the subducting slabs, the mantle wedge temperature, and the presence of some preexisting regional flaws in the overriding plate have been proposed as the deciding factors to ultimately determine the spatiotemporal distributions of arc volcanoes in the overriding plate. For example, England and Katz (2010) showed the location of volcanic front above the slab at the point where the anhydrous peridotite solidus is closest to the trench. Alternatively, Grove et al. (2009) estimated volcano locations as a function of the depth of aqueous fluids released from the subducting plate, the mantle wedge temperature above the region of fluid release, and plate tectonic variables, such as subduction velocity and slab dip. Furthermore, the regular distribution of volcanic centers along the volcanic front line is attributed to various factors, such as regional fracture distribution (Pacey et al., 2013), depth of the magma source (Lingenfelter & Schubert, 1974; Perrin et al., 2018), slab thickness (Marsh, 1975), and heterogeneous melting of the mantle wedge (Yoo & Lee, 2020). Although regional fractures can cause segmentation of the volcanic arc front, there is no spatial correlation between the fracture zones and volcano distribution within an arc segment (Marsh, 1979; Pacey et al., 2013). Several studies, on the other hand, indicate that such regular spacing can be more readily conceived as a result of Rayleigh-Taylor instability (RTI), where the characteristic wavelength of instabilities determines the spacing (Fedotov, 1975; Marsh & Carmichael, 1974; Morishige, 2015).

A line of studies has focused on the transport mechanism of partially molten materials in the mantle wedge to investigate the processes of arc volcanisms, including their spatiotemporal patterns (Aharonov et al., 1995; Pec et al., 2017; Spiegelman et al., 2001; Weatherley & Katz, 2012). However, a number of key questions, especially on the melt transport mechanisms, are yet to be resolved. For example, there is still debate on whether partial melts ascend by forming porosity channels, as observed beneath mid-ocean ridges (Liang et al., 2010; Mandal et al., 2018), and if so, what can be their pathways patterns, or are channels formed by fracturing of the mantle rocks? Several recent studies suggest cold plume formation as a potential mechanism for the upward advection of partially molten materials in the mantle wedge (Codillo et al., 2018; Gerya & Yuen, 2003; Zhu et al., 2009). These materials are less dense than the overburden, and resulting density inversion triggers RTIs, leading to the formation of cold plumes (Figure 1a).

Geophysical studies of subduction zone magmatism (Tamura et al., 2002; Zhao et al., 2009) point to the fact that the cold plume-driven magmatism in subduction zones is essentially a three-dimensional (3-D) phenomenon, where both trench parallel and trench perpendicular plume dynamics need to be accounted for to comprehensively model the partial melt generation and migration. Zhu et al. (2009) have shown from petrological-thermomechanical modeling that slab dehydration initiates small-scale convection to produce numerous cold plumes in the mantle wedge. Based on their simulations, they recognized three types of plumes: (1) closely spaced finger-like plumes, arranged parallel to the trench, (2) ridge-like plumes perpendicular to the trench, and (3) flattened wave-like instabilities parallel to the trench. The viscosity of partially molten zones is found to be the principal factor that controls the type of plume in Zhu et al.'s models. The low-viscosity models (10¹⁸–10¹⁹ Pa s) develop finger-like plumes with a spacing of 30–45 km. The spacing jumps to 70–100 km, and the cold plumes attain sheet-like structures as the viscosity increases by 2 orders of magnitude (10²⁰–10²¹ Pa s).

Despite significant progress in modeling subduction-related cold plumes, there is a lack of systematic investigation to address how far the slab dip might control the flow dynamics in partially molten zones to regulate volcano distribution in the overriding plate. Our present study aims to meet this gap. We investigate the evolution of cold plumes in the framework of 3-D RTIs to explore the origin of the two principal types: linear and areal distributions of arc volcanoes described above. We address the following questions: (1) how does slab dip (α) influence the development of RTIs and thereby determine the modes of plume growth and (2) what is the consequence in the spatial and temporal distributions of arc volcanoes? We use scaled laboratory experiments to demonstrate the effects of α and support the experimental findings with 2-D and 3-D computational fluid dynamics (CFD) simulations. Volcano distributions from the South American (the Andes) (Ramos & Folguera, 2009), the Central American (Mexico) (Stubailo et al., 2012), and the Sumatra-Java subduction system are used to discuss the relevance of our model results. Several studies have reported kiloyear scale frequency in the arc volcanisms, irrespective of their spatial distribution (Kutterolf et al., 2013; Schindlbeck et al., 2018). We show that such episodic eruptions are a consequence of the pulsating ascent behavior of cold plumes.

2 Laboratory Modeling

2.1 Experimental Setup

We developed scaled laboratory models using two immiscible fluids of contrasting densities (ρ = ρ_o/ρ_s) and viscosities (R = μ_o/μ_s); subscripts o and s refer to the overburden and source layer, which represent mantle wedge and partially molten zone, respectively. The density and viscosity ratios are limited in our laboratory experiments by the availability of suitable materials. Two series of laboratory experiments were performed with R < 1 and R > 1, where the first series had ρ = 1.03 and R = 10⁻⁵, while the second series had ρ = 1.13 and R = 25. All the parameters used in the experiments are summarized in Table 1a. For models with R = 10⁻⁵ (called R < 1 type model), we used Polydimethylsiloxane (PDMS) (ρ_s = 965 kg/m³ and μ_s = 10² Pa s), which agrees with the scaled down viscosity (in the order of 10² Pa s) of natural partially molten zones (~10¹⁸ Pa s). We chose water (ρ_o = 998 kg/m³ and μ_o = 10⁻³ Pa s) as the overburden material because it is denser, which is the key mechanical factor for triggering gravitational instabilities, and also it is transparent, allowing us to continuously monitor the three-dimensional evolution of RTIs in the model. Surface tension had an insignificant effect on the RTIs because of the high source layer viscosity.

Table 1a. Model Dimensions and Material Properties Used in the Laboratory Experiments

Model parameters	Symbol	Units	Value
R < 1
Model length	L	cm	60
Model width	W	cm	30
Model height	H	cm	30
Overburden density	ρo	kg/m^3	998
Overburden viscosity	μo	Pa s	10^−3
Source density	ρs	kg/m^3	965
Source viscosity	μs	Pa s	100
Viscosity ratio	R	—	10^−5
Overburden density	ρo	kg/m^3	1,100
Overburden viscosity	μo	Pa s	250
R > 1
Source density	ρs	kg/m^3	970
Source viscosity	μs	Pa s	10
Viscosity ratio	R	—	25

The experimental setup consisted of a rectangular (60 cm × 30 cm × 30 cm) glass box (Figure S1 in the supporting information) filled with water to form the overburden above the source layer. Within the glass box, a wooden rectangular plate (60 cm × 30 cm × 5 cm) was placed in a tilted position to represent slab dip (α) in the model. The overburden above the dipping slab had sufficient space for plume growth. Before placing the plate in the box, a volume of PDMS was spread over its top surface in a dry condition to produce a mechanically coherent layer with uniform thickness. We left the layer undisturbed for 2 to 3 hr to remove air bubbles trapped in the source layer.

The R < 1 type of models does not completely replicate the mechanical settings of natural subduction zones, where the mantle wedge has viscosity higher than the partially molten layer, that is, R > 1. To reproduce such a mechanical setting, we used the second series of models with R = 25 (referred to as R > 1 type hereafter). These models consisted of source layers of hydraulic oil (ρ_s = 970 kg/m³ and μ_s = 10 Pa s) and an overburden of translucent glue (ρ_ο = 1,100 kg/m³ and μ_o = 250 Pa s); both the source layer and overburden materials satisfy the viscosity scaling, as shown in the next section. The major disadvantage of using glue as the overburden is that it is translucent, giving a limited scope to capture the third dimension of the RTIs. However, this type of model provides us good scaling to the natural prototype.

2.2 Model Scaling

We have designed our laboratory experiments fulfilling the requirements of geometric, kinematic, as well as dynamic similarity with the natural prototype (Hubbert, 1937). For geometric similarity, the model length of source layers is scaled to their corresponding length in natural settings, and it yields a length-scale factor (Λ) of 3 × 10⁻⁶ (Marques & Mandal, 2016); the details are provided in supporting information Table S1. For kinematic similarity, the time required for any change in the model needs to be proportional to the time involved in the natural prototype, which in our case is the plume growth time. This is used to estimate the time ratio (Hubbert, 1937). It can be deduced from the equivalent strain rates, as enumerated by Marques and Mandal (2016). The ascent rates of plumes are in the order of 10 cm/year (Gerya et al., 2006; Hasenclever et al., 2011). Accounting the model dimension ratio, this yields the strain rates ratio, ε* = 10¹⁰. Taking time as reciprocal to strain rate, we obtain the time ratio in our model: τ = 10⁻¹⁰ (Table S1). As the inertial forces in the present case are negligibly small, the main controlling factor for dynamic similarity is the body force due to gravity and leads to the ratio of the acceleration due to gravity being unity. We can choose model dimension, mass, and time ratios: Λ, M, and τ independently, without violating the dynamic similarity. For our model, the dynamic scaling must satisfy a specific viscosity ratio, given by

(1)

where ρ* is the density ratio (0.37) (Table S1). Equation 1 yields the viscosity ratio (μ*) in the order of 10⁻¹⁶. Considering the viscosity as ~10¹⁸ Pa s (Zhu et al., 2009), the scaling factor yields the model material viscosity as ~10² Pa s, which is the viscosity of PDMS used for the layer in our model.

For experiments with R = 25, we use the same length-scale ratio (Λ) and similar density ratio (ρ*) factor but have the timescale lower by 1 order (i.e., τ = 10⁻¹¹) (supporting information Table S2). This leads to a viscosity ratio of 10⁻¹⁷ (Equation 1). The scaling factor gives a source layer viscosity of 10 Pa s (cf. viscosity of hydraulic oil) (Table S2). Considering R = 10², the overburden viscosity should be 10³. We chose translucent glue (μ_o = 250 Pa s) as the overburden to obtain the scaling factor closest to our desired value (~10³).

2.3 Experimental Runs and Quantitative Analysis

In conducting the laboratory experiments, two main parameters were considered: source layer dip (α) and source layer thickness (T_s). In the first series of experiments with R = 10⁻⁵, α was systematically varied between 10° and 60° at an interval of 10°. For a given α, we chose T_s = 0.5, 1, and 1.5 cm, which scale to ~1.7, ~3.3, and ~5.2 km thick partially molten zones, respectively, in natural settings (Table S3). In the second series of experiments with R = 25, α was varied in the range 10° to 40° at an interval of 10° with T_s = 0.5, 1 cm (Table S3).

For postprocessing of the model observations we used a set of four parameters to quantitatively present our experimental results. (1) Normalized wave numbers of instabilities: A time series analysis of this parameter from the experimental runs (supporting information Section S3) was performed to show how 3-D instabilities grow in size with ongoing process. This analysis also allows us to assess the degree of wave coalescence in their geometrical evolution. (2) Wavelength ratio of RTI waves along and across the slab strike: This ratio is used to quantitatively express the 3-D shape of RTIs in the source layer as a function of slab dip and consequently to characterize the contrasting modes of RTIs. The actual and upscaled values of wavelengths are given in supporting information Table S3. (3) Updrift and plume growth velocities: These kinematic parameters were estimated from the mean velocities of domes and plumes, respectively (actual and upscaled values given in Table S3). They are used as a measure of the relative transport rates in the source layer under varying slab dips (α). We present this kinematic analysis specifically for the R > 1 type of models as they provide a better approximation to natural subduction system. (4) Plume distance: This parameter is used to quantitatively compare volcano separation in model and in natural settings.

2.4 Modes of Plume Growth

In our laboratory models, plumes evolved in three stages (Figure 1b), which are described using a normalized experimental runtime (t* = t/t_T, where t_T is the total runtime, and it is noted that instabilities almost ceased to occur in the source layer after t_T). Stage I (t* = 0–0.2): RTIs developed a train of waves along the slab dip direction with a characteristic wavelength λ_L (called longitudinal waves hereafter), followed by another set of RTI waves orthogonal to λ_L waves (called transverse waves) with a characteristic wavelength λ_T. Stage II (t* = 0.2–0.6): λ_T and λ_L waves progressively interfered to form 3-D instability structures, characterized by a series of domes. Stage III (t* > 0.6): the domes grew vertically to form spatially scattered plumes (areal distribution). We describe this mode of plume formation by λ_T and λ_L interference as Mode 1. The other mode (called Mode 2) reflects that RTIs dominated by λ_L waves, with little or no growth of λ_T waves, produced an array of plumes (linear distribution) preferentially at the upper edge of the source layer.

2.5 Reference Model—Mode 1

The reference model (α = 20°, T_s = 0.5 cm, and R = 10⁻⁵) for Mode 1 plumes is shown in Figure 2a. In Stage I, the RTIs produced sequentially longitudinal and transverse waves with λ_T > λ_L (e.g., λ_L ~ 6 km and λ_T ~ 11 km) (Figure 2a-1), where λ_T/λ_L ratios lie between 1.8 and 2.5 (Figure 3c). In Stage II their interference gave rise to approximately regular 3-D wave structures in the source layer (Figure 2a-2), which underwent geometrical transformation in time with progressively reducing wave numbers in both longitudinal and transverse directions, for example, from 0.73 to 0.42, whereas from 0.86 to 0.64 (Figures 3a and 3b, blue lines). These transformations resulted mostly from lateral coalescence of the domes. As λ_T was always larger than λ_L, it formed an overall linear trend of the RTI waves along the slab dip direction (Figure 3c). The waves progressively amplified to produce nearly periodic arrays of elongate domes (Figures 2a-3 and 2a-4), each dome covering an area of ~13 × 7 km (in transverse and longitudinal direction, respectively). The RTI structures ultimately preserved a smaller number of large elongate domes (15 × 11 km) with transverse and longitudinal spacing around 11 and 6 km. These large domes subsequently transformed into asymmetrical shapes, verging to the updip direction (Figure 2a-5). In a given time interval (0.5 Ma), some of them (1 to 2 out of 10 domes) selectively grew vertically at faster rates (15 cm/year) to form typical plumes, leaving the rest in a dormant state (Figures 2a-4–2a-6). A plume remained active for a finite time period (0.1 Ma) and then pinched out, facilitating nucleation of another plume elsewhere in the source layer. This is how plumes developed randomly in space and time to form a spatially distributed (Mode 1) pattern.

Figure 2

Laboratory reference models with R = 10⁻⁵ and T_s = 0.5 cm showing the evolution of (a) Mode 1 plumes for α = 20° and (b) Mode 2 plumes for α = 40°.

Figure 3

Experimental models showing (a) variations of normalized transverse wave numbers ( ) with normalized experimental run time (t*) for varying slab dips (α). (b) Variation of normalized longitudinal wave numbers ( ) with t* for different values of α, where wave number k = 2π/λ. (c) Estimated plots of λ_T/λ_L with α. (d) Variations of the updrift velocity and plume growth velocity with α. (e) Histograms of trench perpendicular and trench parallel distances of plumes obtained for both R < 1 and R > 1.

Figure 4

Development of RTIs in analog experiments with R = 10⁻⁵ for varying slab dips (α = 10–40°) and a constant source layer thickness (T_s = 0.5 cm). (a) The λ_T/λ_L wave interference in the initial stage (Stage I), leading to extensive dome formation in the source layer in the intermediate stage (Stage II), and their selective vertical growth into plumes (Mode 1) in the advanced stage (Stage III). (b) The λ_T/λ_L wave interference, dominated by λ_L instability to form downdipping RTIs in Stage I, followed by formation of trains of asymmetric elongate domes in Stage II, and subsequent growth of Mode 1 plumes in Stage III. (c) Formation of elongate λ_L instability in Stage I, prompting updip material advection to nucleate plumes at the upper edge of the source layer in Stage II and their subsequent growth in Stage III. (d) Growth of strongly elongated λ_L wave instability in Stage I, focusing the updip advection to localize periodic domes at the upper edge in Stage II, and their rapid growth into matured plumes in Stage III.

2.6 Reference Model—Mode 2

We present another reference model (α = 40°, T_s = 0.5 cm, and R = 10⁻⁵) to show the evolution of Mode 2 plumes (Figure 2b). During Stage I, RTIs were dominated by λ_L waves, showing insignificant growth of λ_T waves (Figure 2b-1). They eventually gave rise to linear ridge structures in Stage II, where each ridge acted as a conduit to channelize flows in the source layer. This process initiated trench perpendicular updip advection of the buoyant fluid. Updip advection reduced the wave coalescence, reflecting much smaller variations of the longitudinal wave number ( from 0.94 to 0.8) (Figure 3b, magenta line), but prompted RTIs to localize domes preferentially at the upper terminal edge of each λ_L wave (Figure 2b-2). In Stage III, the domes grew vertically to form Mode 2 plumes with a characteristic spacing (50–55 km, Figure 2b-3), controlled by λ_L. Each plume in the linear distribution trailed into downdipping ridges, which acted as feeders to supply the buoyant fluids into the growing plumes (Figure 2b-4).

2.7 Mode 1 to Mode 2 Transition

We describe here a set of laboratory experimental models (R = 10⁻⁵) for α = 10° to 40° to show how and at what threshold α values (i.e., α*) the Mode 1 to Mode 2 transition occurs. At α = 10°, RTIs developed plumes in Mode 1 (Figure 4a) (Stages I and II), where λ_T > λ_L (λ_T/λ_L = 1.2–2) (Figure 3c), and the λ_T-λ_L interference formed domes globally in the source layer (Stage II). During their growth, they drifted at low rates (3–3.4 cm/year) toward the updip region of the slab (Figure 3d). In places, the process of dome coalescence reduced their spatial density in the source layer as revealed by significant decrease in the wave numbers (0.62 to 0.37) and (0.71 to 0.54), respectively (Figures 3a and 3b, black lines). In Stage III the model produced typical Mode 1 plumes that grew vertically at relatively slow rates (8.1–8.6 cm/year) (Figure 3d) and had average transverse and longitudinal distances of 80–100 and 35–45 km (Figure 3e), respectively.

Increasing α resulted in quantitative changes in the RTI structure (Figure 4b). For α = 20°, λ_T/λ_L ratios became 1.8 to 2.5 (Figure 3c), and the interference of longer λ_T waves with λ_L waves gave rise to persistent ridges with their long axis parallel to the slab dip direction. In addition, the coalescence process became significantly weaker; the wave numbers thus underwent relatively less changes ( : 0.73 to 0.42 and : 0.86 to 0.64) in Stage II, as compared to the α = 10° model (Figures 3a and 3b, blue lines). However, the λ_T instability was active enough to form the 3-D wave geometry, characterized by regularly spaced elongate domes. Each dome drifted in the updip direction tracking the λ_L crest lines at faster rates (5–6.8 cm/year) (Figure 3d). In Stage III, these drifting domes grow vertically to produce Mode 1 plumes at average transverse and longitudinal distances of 60–95 and 40–50 km, respectively (Figure 3e). Compared to plumes in the α = 10° model, they ascended at much higher rates (13–16 cm/year) (Figure 3d).

Further increase in α to 30° showed a transition from Mode 1 to Mode 2 RTI evolution (Figure 4c). The model produced λ_L waves in Stage I, which amplified rapidly to form a train of down dipping ridges with regular spacing. The transverse waves appeared with λ_T ≫ λ_L (λ_T/λ_L > 3) (Figure 3c), but they had a weak interference with λ_L to form gentle asymmetric domes. In Stage II, the domes had little tendency to grow vertically as the λ_T waves ceased to amplify with time; they rather updrifted at high velocities (10–12 cm/year) (Figure 3d). The wave numbers, in longitudinal and transverse directions went through small changes; to 0.49 and :0.9 to 0.7 (Figures 3a and 3b, red lines). The λ_L waves acted as effective conduits to channelize the buoyant materials to localize the domes preferentially at their upper ends (Figures 4c-II and 4c-III). These domes were arranged along a trench parallel linear trend at a spacing of 30–40 km, in consistent with λ_L (~30 km), and they produced Mode 2 plumes with an average longitudinal distance of 40–45 km (Figure 3e), leaving the source layer almost free from any instabilities down the slab dip in Stage III. The plumes had characteristically high ascent rates (21–25 cm/year) (Figure 3d). The λ_T wave instability practically disappeared when α ≥ 40° (Figure 4d). The value of remained almost constant throughout the experiments (Figure 3a, magenta line). The growth of λ_L in such a condition greatly facilitated the rapid development of Mode 2 plumes (26–28 cm/year) (Figure 3d), trailing into a series of parallel linear ridges with spacing ~40 km, plunging down the slab dip direction (Figure 3e).

We also varied initial thickness (T_s) of the source layers, keeping the slab dip constant (e.g., α = 20°). For a small thickness (T_s = 0.5 cm), the model developed globally both λ_L and λ_T wave instabilities, which interfered with one another to produce elongate domal structures (Figure S4a). The domes drifted updip, albeit at slow rates, and some of them grew vertically to form Mode 1 plumes. However, most had limited vertical growth rates owing to sluggish updip material supply into their roots. Instead they produced isolated elongate ridges, plunging down the slab dip (Figure S4a). Increase in T_s (T_s = 1.5 cm) facilitated the updrift of domes produced by λ_L-λ_T interference (Figure S4b). Some of them rapidly amplified into plumes while migrating upward and formed a cluster of matured plumes in the upper region of the dipping slab. Unlike Mode 2 plumes, they are scattered across the trench. Large T_s enhanced updip material advection and continuously supplied materials to sustain an uninterrupted growth of the plumes.

2.8 Applicability of the Model Results for R > 1

To test how far the experimental results obtained from the R < 1 type of models apply to an actual subduction setting, we used the R > 1 type of model and found qualitatively similar results. To demonstrate this, we present here two specific models with R = 25 for low (α = 20°) and high (α = 30°) angle slab dips. For α = 20°, the RTI produced 3-D wave structures, forming several regularly arranged domes in the source layer. They subsequently grew vertically to produce distributed plumes (Mode 1) (Figure 5a), as in the R < 1 models (Figure 4). However, the growth rate of plumes in case of R > 1 was relatively low (15 cm/year, as compared to 20 cm/year for R < 1, supporting information Figure S7). The estimated average longitudinal and transverse plume spacing was found to be 45 and 60 km, respectively, which are in agreement with the R < 1 model results (Figure 3e). For α = 30°, the RTI produced a dominant set of λ_L waves, as in R < 1 models. These waves evolved into linear ridges along the slab dip direction, which subsequently gave rise to a linear distribution of Mode 2 plumes (Figure 5b). Their spacing varied from 40 to 50 km (Figure 3e), broadly matching the value obtained from the R < 1 models. Models with R > 1 produced flattened plume heads, in contrast to rounded plume heads in case of R < 1. However, the threshold value for Mode 1 to 2 transition (α*) remains unchanged.

Figure 5

Development of Mode 1 and Mode 2 plumes for low-angle and high-angle slab dips analog experiments with R = 25 and T_s = 0.5 cm. The value of λ_T typically varies from 10 to 60 km.

3 CFD Simulations

3.1 Model Design

We performed 2-D CFD simulations considering two-phase fluid models, consisting of a source layer (phase 1) and mantle wedge (phase 2). We employed the conservative level set method to track the evolving phase interface between the two immiscible fluids. Our CFD modeling used two governing equations: the Navier-Stokes equation and the continuity equation. These equations were solved using commercial finite element code (COMSOL Multiphysics, 2015) (details given in supporting information Sections S8 and S9). Several earlier workers used this code for large-scale modeling in geodynamics (Dutta et al., 2016; He, 2014; Ryu & Lee, 2017). We ran two types of CFD simulations: (1) models with dimensions and material parameters, corresponding to the laboratory setup and (2) models approximated to the natural prototype. The first type was used mainly to validate our laboratory findings. The models had a horizontal dimension of 60 cm and a vertical dimension of 30 cm, chosen to reproduce the laboratory model dimensions. We performed laboratory-scale model simulations for both R < 1 and R > 1 with α = 20° and 30° and T_s = 1 cm (model parameters given in Tables 1a and 1b).

Table 1b. Description of the Values of Different Model Parameters Used in CFD Simulations

Parameter	Units	Melt layer	Overburden mantle
Density	kg/m^3	2,800–3,100	3,300
Viscosity	Pa s	10^17	10^19–10^22
Thickness	km	2–6	50–300
Subduction angle (α)	(deg)	10–40	—

The second type of CFD models covered a trench perpendicular section with a horizontal (x) dimension of ~350 km and vertical (y) dimensions of 110 to 330 km, depending upon the slab dip (10° to 40°) (Figure S8). For 3-D simulations, we extended the 2-D geometry in a z dimension (~200 km) parallel to the trench. These models contained a low-viscosity (10¹⁷ Pa s) and low-density (3,000 kg/m³) source layer at the interface between the dipping slab and the overlying mantle wedge (Table 1b). Based on the available data in published literature (Gerya & Yuen, 2003; Marsh, 1979), we chose the source layer thickness to vary in the range 2 to 6 km. We introduced initial geometrical perturbations at the interface between the source layer and the overburden (small seed and sinusoidal type perturbations, details provided in supporting information Figure S11) with a very small amplitude (~40 m) and varying wavelengths (10 to 60 km) (Evans & Fischer, 2012; Mancktelow, 1999; Schmalholz & Schmid, 2012). The bottom and top model walls were assigned a no-slip condition, keeping the sidewalls under a free-slip condition. The estimated Reynolds number (Re) in our model was found to be in the order of Re ~ 10⁻¹⁹, which ensures the choice of model boundary conditions and parameters with a good approximation to the natural prototype (Hasenclever et al., 2011; Zhu et al., 2009). All the relevant model parameters and material properties are summarized in Table 1b and supporting information Table S4.

3.2 Laboratory-Scale Simulations

The laboratory-scale CFD models for R < 1 (R = 10⁻⁵) produced Mode 1 plumes for low-angle slab dips (α < 30°) and Mode 2 when the slab dip angles became large (α ≥ 30°) (Figure S9). This Mode 1 to 2 transition at α* = 30° is in excellent agreement with the experimental value of threshold slab dip ~30° (Figures 4b and 4c). The plumes drifted updip, and the rate increased with increasing α, for example, it was 0.8 cm/min (upscaled 13 cm/year) for α = 20°, which increased to 1.2 cm/min (20 cm/year) when α = 30° (details provided in supporting information Section S9). These estimates match our experimental values (8.5–23 cm/year) (Table S3). The CFD models for R > 1 (R = 25) also showed Mode 1 to 2 transition with increasing α (Figure S9). To summarize, the Mode 1 to 2 transition occurs as a function of slab dip angle, irrespective of R > 1 or < 1.

3.3 Large-Scale Simulations

To extrapolate our laboratory experiments and their equivalent CFD model results to natural subduction zones, we used the second type of CFD simulations. Here we present a set of simulations run with α = 10° to 40° keeping T_s = 4 km, R = 10², and Δρ = 300 kg/m³ (Table S4). For α = 10°, the RTI develops globally in the form of a series of regularly spaced domes down the slab dip direction (Figure 6a). The domes grow more or less simultaneously in the vertical direction, albeit at varying rates (12 to 14 cm/year) (Figure 7c, red line) to produce an array of Mode 1 plumes. Low-angle slab dips promote RTIs to occur in multiple generations, forming several secondary plume pulses, which are discussed later. The pulsating plumes show little or no updrift as they attain a mature stage. Models with α = 20° produce similar Mode 1 plumes (Figure 6b). However, steepening of α results in some quantitative changes both in their geometry and kinematics. First, the RTIs do not occur in multiple generations, and the plume frequency in the source layer is reduced. Second, Mode 1 plumes show a strong spatial variation in their growth rates; plumes located in the updip region grow faster (16 cm/year) than those further down the slab (10 cm/year). Tall, mature plumes concentrate mostly in the shallow part of the source layer, as observed in our physical experiments (Figures 4 and 5). At α* = 30°, the RTI undergoes a transition from Mode 1 to Mode 2 (Figure 6c). The instabilities in the source layer form a series of domes in the downdip direction, but they hardly grow vertically; rather, they drift up dip to coalesce sequentially with the growing plume at the upper edge. This process results in pulsating ascent behavior of Mode 2 plumes. Due to this active material transport, Mode 2 plumes grow at higher rates (~29 cm/year) (Figure 7c, green line). For α = 40°, the RTIs localize exclusively at the upper edge of the source layer to form a row of Mode 2 plumes (Figure 6d). The undisturbed part of the layer acts as a passage for updip material advection to sustain the plume growth at high rates (35 cm/year) (Figure 7c, black line). We ran 3-D CFD models with α = 40° (details presented in supporting information Section S10) to confirm the growth of λ_L waves observed in the laboratory experiments (Figures 2 and 4). They reproduced a set of parallel ridge-like instabilities down the slab dip direction that focused the upward partial melt advection in the source layer, as also observed in earlier numerical models (Zhu et al., 2009).

Figure 6

CFD simulations showing the growth patterns of large-scale RTIs from dipping source layers (T_s = 4 km) in subduction zones for α = 10–40° (a–d). It is noteworthy that the transition from Mode 1 to Mode 2 as α reaches 30°, as observed in physical experiments (Figure 4).

Figure 7

Calculated plots from numerical models to show plume growth rate as a function of the following parameters: (a) slab dip (α) for different density contrast (Δρ), (b) viscosity ratio (R) for different values of α, (c) uniform source layer thickness (T_s) for different α values, (d) slab dip for given plate velocity and nonuniform source layer thickness, and (e) volume of partially molten material pulses as a function of α and run time.

3.4 Parametric Analysis

We varied the density contrast (Δρ) between the overburden and the source layers from 200 to 500 kg/m³ to investigate the buoyancy effects on the mode of plume growth. The overall plume dynamics remains unaffected by Δρ, and the Mode 1 to 2 transition occurs at the same threshold slab dip (α* = 30°). However, their ascent rates significantly increase with increasing Δρ, for example, 12.5 to 21.5 cm/year from 200 to 500 kg/m³ at α = 20° (Figure 7a).

We investigated the role of viscosity ratio R in controlling the evolution of plumes. Increasing R lowers their ascent velocity, for example, ~18 cm/year for R = 10³, which decreases to 8.5 cm/year when R = 10⁵, when α = 20° (Figure 7b, blue line). This effect of viscosity ratio can be attributed to a higher viscous resistance to the ascending plume head by the overburden. However, the threshold slab dip for Mode 1 to 2 transition remains unaffected by R. Decreasing R below 10² again reduces the ascent velocity, possibly due to higher viscous resistance within the source layer. The plume ascent rate becomes maximum for R = 10³ (Figure 7b).

A series of simulations were run to study the effects of source layer thickness (T_s) keeping slab dip (α) fixed (Figure 7c). For α = 10°, the ascent rate of plumes is nearly 4 cm/year for T_s = 2 km; the rate increases to 25 cm/year when T_s = 6 km. Most of the models in our present study dealt with a source layer of uniform thickness. Earlier studies suggested that partially molten zones in natural subduction settings can progressively thicken with depth (England & Katz, 2010; Grove et al., 2012). To investigate the possible effects of nonuniform thickness, we ran simulations with T_s varying down the slab dip (4 km at 70 km to 10 km at 150 km), for different α. For α = 20°, the simulations showed a higher ascent velocity of plumes (20 cm/year) than for uniform T_s (15 cm/year) (Figure 7d, black line as compared to the blue line). Increase in α to 30° widens their difference, 30 (uniform T_s) to 37 cm/year (nonuniform T_s) (Figure 7d, black line). However, the overall Mode 1 to Mode 2 transition with α occurs in the same fashion (Figure S13).

In a set of simulations, we introduced a slab motion (3 cm/year), as applicable to natural subduction settings (details provided in supporting information Section S12). The slab motion influenced mostly the overall plume geometry to attain an updip convex curvature. However, it hardly affected the threshold slab dip for Mode 1 to Mode 2 transition. The plume growth velocity also remained unaffected, but their updrift velocity dropped from 15 to ~10 cm/year when α = 20° (Figure 7d, red line).

Our estimates suggest that increasing slab dip promotes the material volume (V_H) transport in pulses on a timescale of ~0.3 Ma (Figure 7e). For α = 10°, the maximum V_H in a single pulse is 1,310 km³, increasing to 7,518 km³ when α = 40°. However, V_H does not significantly change with other parameters such as density contrast and viscosity ratio (supporting information Figure S14). Considering 5% of the plume volume as eruptible partial melts, a plume pulse is expected to produce volcanic magmas in the order of 67–376 km³, which is in agreement with the dense rock equivalent reported from several modern subduction zones (Kimura et al., 2015; Umeda et al., 2013). Steepening of slab dip angle from 10° to 40° can thus increase the magma volume by ~6 times.

4 Discussion

4.1 Comparison of Laboratory, Numerical Model and Natural Observations

We compared our experimental and numerical model results for R = 25 with the available data from natural subduction zones. The initial values of plume growth rate in the range 8 to 15 cm/year (Figure 8a, red line), predicted from numerical models for α = 20°, agree well with the laboratory results (9–12 cm/year) (Figure 8a, blue line). Our model estimates are consistent with the ascent rates (6 to 14 cm/year) provided by Gerya et al. (2006) and Hasenclever et al. (2011).

Figure 8

(a) Validation of the numerical (R = 10² and Δρ = 300 kg/m³) and experimental (R = 25) plume growth velocities with published data. (b) Comparison of the areal density of plumes from analog experiments (R = 25 and T_s = 0.5–1.0 cm) with that of volcanoes from different subduction zones. (c) Comparison of longitudinal and transverse plume spacing from our analog (R = 25 and T_s = 0.5–1.0 cm) and numerical experiments (R = 10², T_s = 2–6 km, and Δρ = 300 kg/m³) with natural volcano spacing from different subduction zones. (d) Analysis of the timescale of frequency of plume ascent from numerical and experimental results (model properties same as that of c).

We also chose the spatial density of distributed (Mode 1) plumes produced in our laboratory experiments with low-angle slab dips to compare them with natural data. From Google Earth Pro we calculated the spatial density of volcanic spots, measured as the number of volcanic spots per 1,000 km² in important subduction zones. For example, in the Mexican subduction system densities range from 0.4 to 0.49, whereas they range from 0.53 (West Java) to 0.6 (East Java) in the Java trench. The Andean subduction zone displays scattered volcanic spots with their spatial density varying from 0.58 (Paro) to 0.8 (Punakha) (Figure 8b). Similarly, we calculated the plume density (number of plumes per unit area of the source layer) from our laboratory models with R = 25 and T_s = 0.5–1.0 cm using their plan view images. The upscaling of our laboratory estimates yield a spatial density of 0.35–0.7 per 1,000 km² (Figure 8b), which is in agreement with the data for natural subduction settings discussed above.

The volcanic arc distributions in natural subduction zones broadly fall into two distinct categories: (1) regularly spaced volcanic centers, forming a distinct trench parallel arc, similar to Mode 2 plume distribution obtained from our laboratory models with steep slab dips (α ≥ 30°), and (2) scattered distribution with volcanoes spread both parallel and perpendicular to trench similar to Mode 1 plume distributions produced in our models with gentle dips (α < 30°). We consider volcano spacing as a parameter to compare with the plume spacing obtained from the experimental (for R = 25 and T_s = 0.5–1.0 cm) and numerical (for R = 10², T_s = 2–6 km, and Δρ = 300 kg/m³) results. The longitudinal and transverse plume spacing in laboratory experiments (upscaled) is found to be 35–75 and 44–105 km, respectively (Figure 8c). On the other hand, our numerical simulations show a longitudinal plume spacing of 33 to 50 km in 3-D models and transverse plume distance of 70–90 km in 2-D models. A compilation of the estimates from α < 30° natural subduction zones suggests that the spacing of volcanic centers ranges from 32 to 60 km and 48 to 100 km in the longitudinal and transverse direction, respectively (Figure 8c) (Table S5). This marked similarity in the estimates validates our models.

We have also compared timescales of periodicity of pulsating events recorded in natural subduction zones with those predicted from our experimental and numerical models. The frequency of natural volcanic events (300–500 kyr) closely matches with the experimental (270–520 kyr, upscaled) and numerical (270–510 kyr) model estimates (Figure 8d). We discuss the timescale of episodic volcanisms more in detail in section 4.4.

4.2 Geological Relevance of the Model Parameters

Slab dip variability is a common feature of natural subduction zones throughout the globe. Such variability can even occur within a single subduction zone along the trench line (Lallemand et al., 2005). Several convergent plate boundaries, such as the Mexico subduction system (Currie et al., 2002), the southern Ecuador subduction (Gailler et al., 2007), and the Pampean flat subduction (Ramos et al., 2002), show low slab dip angles (10° to 25°). In contrast, there are many boundaries, such as the Western Sunda and the Kamchatka plates, which display high-angle slab dips (α ≥ 30°) (Chiu et al., 1991; Hall & Spakman, 2015). In our modeling, we thus consider α as the principal model parameter to explore how low-angle versus high-angle subduction dynamics can influence the RTIs in the partially molten zones produced by dehydration melting. Experiments with α < 30° suggest that low-angle subduction would produce an areal distribution of the RTIs (Figures 4a and 4b), involving relatively small updip advection of the partially molten materials. Steepening of α (≥ 30°) weakens the global RTIs to facilitate the advection process that eventually leads to RTIs localization at a shallow depth along the upper fringe of the partially molten zone, as observed in our experimental models (Figures 4c and 4d) and CFD simulations (Figures 6c and 6d), as well as earlier numerical models (e.g., Zhu et al., 2009). One of the major implications of this finding is that high-angle subduction cannot readily produce plumes from the partially molten materials in deeper sources. Under these circumstances, materials advect to accumulate in the updip region and form Mode 2 plumes at a shallower depth.

It is worth discussing that the trench normal width of volcanic belts in a subduction zone should depend on the steepness of slab dip from a geometrical point of view; this width represents the horizontal projection of plume distances on the source layer as a cosine function of α (Marsh, 1979). Steepening of the slab dip would reduce the transverse plume distance measured on the horizontal upper surface. But in this study, we have shown that the Mode 1 to 2 transition in RTIs at α ≥ 30° leads to a drastic transformation of the distributed plume pattern into a focused one (Figure S3, blue line). If the focusing would occur solely due to the geometrical relation, α must be 70° or more (Figure S3, red line). Both our model and natural observations suggest that focused arc volcanism can occur at much lower values of α due to the transition in RTI mode.

Many natural subduction zones, for example, the Mariana, the East Caribbean, and some parts of the Java-Sumatra subduction zones (Chiu et al., 1991; Deville et al., 2015; Hall & Spakman, 2015), steepen their dips to nearly vertical orientations at greater depths. Both analog and CFD model results suggest that the RTI patterns would remain qualitatively unchanged when α > 30° and always give rise to a linear distribution of plumes at the upper edges of source layers, leaving the down slab region completely undisturbed. Further steepening of slab dip angle (i.e., α > 40°) does not cause any qualitative change in the RTIs. We therefore restricted our experimental runs within α < 60° (Table S3).

Petrological calculations have predicted dehydration reactions in the subducting slabs, resulting in partial melting within a narrow zone at the interface of slab and mantle wedge (Grove & Till, 2019; Till et al., 2012). Such partially molten zones generally begin at a depth of 70 to 160 km and cover a distance of 70 to 200 km along slab dip, giving rise to a mechanically distinct layer atop the dipping slab (Grove et al., 2012; Schmidt & Poli, 1998; Ulmer & Trommsdorff, 1995). For our natural-scale CFD modeling, we thus fixed the upper extremity of partially molten regions at a depth of 70 km (Gerya et al., 2006). The maximum stability depth of different water-bearing phases varies depending upon the subduction angle (α) and subduction velocity as they can modify the thermal structure in the mantle wedge, and thereby the downward extent of partially molten zones. However, the RTI mode is found to be sensitive not to the areal coverage of the partially molten zone but its thickness. We varied the partially molten zone thickness (T_s) from 2 to 6 km in CFD simulations and their scaled equivalence in our laboratory experiments. Earlier studies modeled the partially molten zones as 1 to 10 km thick layers (Gerya & Yuen, 2003; Marsh, 1979). The two most important petrological factors in controlling T_s are (1) the volume of H₂O-rich fluids released from the subducting slab and (2) the thermal structure in the mantle wedge. For a given thermal structure, increasing fluid volumes would result in higher degrees of dehydration melting to produce thicker partially molten zones. According to our experiments, increasing T_s facilitates domes to drift up the slab, ultimately forming a cluster of plumes at shallow depths. This kind of plume clustering occurs in a particular region of the Mode 1 field defined by T_s and α (Figure 9), causing a decrease in transverse plume separation. This ultimately leads to Mode 1 to Mode 2 transition at a lower value of α (~20°) for large T_s (~1.5 cm in our experiments) (Figure 9).

Figure 9

A regime diagram of the two modes of plumes as a function of source layer thickness (T_s) and slab dip (α) for R < 1.

4.3 Volcanic Arc Patterns in Subduction Settings

The Andean subduction system offers an excellent opportunity to study the control of slab dip in interpreting the volcanic distributions in space and time. This system presently involves Nazca plate, subducting with laterally varying slab dips along the N-S trending trench on the western margin of the South American overriding plate (Figures 10a and 10b). There are three flat slab segments: Bucaramanga, Peruvian, and Pampean, which separate the arc segments with high-angle slab dips (α > 35–50°), marked by localization of three distinct volcanic belts: The northern, the central, and the southern volcanic zones. Each of these segments displays a trench parallel linear distribution of closely spaced volcanic spots (Ramos & Folguera, 2009). Both our laboratory experiments and CFD simulations suggest that they originated from Mode 2 plumes (Figures 4 and 6). By reconstructing the past subducting plate configuration of the Andean subduction zone, we find a completely different slab configuration of the Andes, which provides indications for past flat slab subduction. Based on geological evidence, Ramos and Folguera (2009) have established a series of flat slab segments, covering the entire stretch of the Andean system. From north to south, these are Bucaramanga, Carnegie, Peruvian, Altiplano, Puna, Pampean, and Payenia flat slab segments. The three segments: Bucaramanga, Peruvian, and Pampean maintained a low angle slab dip from 13, 11, and 12 Ma, respectively, to the present day, whereas the other segments were flat during different time intervals (Carnegie: <3 Ma; Altiplano: 40–32 to 27–18 Ma; Puna: 18–12 Ma; and Payenia: 13–5 Ma). For the present discussion, we specifically choose three segments: Puna, Pampean, and Payenia to compare their volcanic distribution patterns with those observed in our models. The Pampean flat slab segment, flanked by the Puna segment on its north, shows a contrasting volcanic arc pattern (Figure 10a). The Puna segment was flat during 16–12 Ma (Kay & Coira, 2009; Martinod et al., 2010; Ramos & Folguera, 2009) and steepened after 12 Ma to attain the current dip of 30° (Martinod et al., 2010). On the other hand, the Pampean had a high-angle slab dip before 16 Ma and continuously lowered its slab dip to achieve an almost flat present configuration. These two segments evolved through opposite trends in their slab dips, which are shown by their contrasting temporal volcano distributions. The volcanic spots in the Puna segment are more densely clustered than those in the Pampean segment. During the period of flat subduction (>12 Ma; Figure 10a, X2), the slab beneath the Puna segment produced Mode 1 plumes. Slab dip steepening after 12 Ma facilitated domes to updrift and form Mode 2 plumes (Figure 10a, X1). The volcanic activities presently focus into a narrow region constituting a sharp volcanic arc in front of the Peru-Chile trench (Figure 10a). In contrast, the Pampean segment had a high-angle slab dip prior to 12 Ma, which focused the volcanic activities into a narrow frontal region. The onset of slab flattening after 12 Ma prompted the volcanic spots to spread down the slab (Figure 10a, Y3–Y1) (Kay et al., 1991; Ramos & Folguera, 2009; Ramos et al., 2002). We interpret this switch over as a consequence of Mode 2 to Mode 1 transition in plume dynamics in response to a progressively reducing slab dip. The age distributions of volcanoes support this proposition. The segment displays a line of 15 Ma volcanic spots that possibly indicates the phase of focused volcanism by Mode 2 plumes (Figure 10a, Y3). All the younger volcanic spots <12 Ma are strongly scattered, showing no consistent space-time correlation. Our laboratory models produce matured Mode 1 plumes randomly in space and time, which are in agreement with the scattered age distribution of volcanic spots in the Pampean segment.

Figure 10

Spatiotemporal distributions of arc volcanisms in the Puna, Pampean, and Payenia region of the Andes. (a) Locations of the Puna and Pampean flat slab segment in the Central Andes with 100 and 200 km isobaths of the Nazca plate and with an outline of main basement uplifts of Sierras Pampeans and location of the Precordillera fold and thrust belt and representative ages of volcanoes (modified after Ramos et al., 2002, and Ramos & Folguera, 2009). (X1) Cross section shows the present-day subducting plate configuration and associated volcanic locations. (X2) The 16–11 Ma configuration of the same plate with distributed volcanic spots (after Kay & Coira, 2009). (Y) Schematic cross sections of the plate segment between 30° and 31°S. Three sections (Y1, Y2, and Y3) show transformation of arc volcanism from localized to distributed arc volcanisms with decreasing subduction dips (α) through time (20–16 to 9–6 Ma) (reconstructed from Kay et al., 1991). (b) Variation of the magmatic arc pattern from Miocene (10 Ma) to Holocene (2 Ma) in the Payenia region. Z1: present configuration of the subducting plate at 37°S; Z2: its Miocene reconstruction (after Gianni et al., 2017).

The Payenia segment displays two distinct patterns. Late Miocene arc volcanoes are scattered in both trench parallel and trench perpendicular direction, covering a horizontal distance of ~400 km (Figure 10b, Z2). By contrast, the present-day volcanic arc defines an excellent trench parallel linear front (Figure 10b, Z1). These two patterns correspond to Mode 1 and Mode 2 plumes, respectively, similar to our model results. During the period (13–5 Ma) of flat slab subduction in the Payenia segment, Mode 1 plumes formed randomly as observed in our models with α < 30° (Figure 4). With steepening in slab dips, the updip advection became a dominating process to promote Mode 2 plumes in the upper fringe of the partially molten layer. Our experimental models produced Mode 2 plumes with a regular spacing, controlled by λ_L wave periodicity. We invoke this plume dynamics to explain the regular pattern of the volcanic arc front. The average spacing of volcanic spots in the front is estimated in the order of 40–60 km, which is in agreement with the scaled-up values of longitudinal plume spacing (35 to 70 km) obtained from the laboratory models.

The Central American trench and the Java trench and their current subducting plate configurations are well constrained from seismic sections that we can use to demonstrate the effects of slab dip on the volcano distributions. In the Central American trench, the Cocos plate subducts beneath the overriding North American plate, with laterally varying slab dips on a stretch of about 700 km (Figure 11a), high-angle slab dip (~45–48°) on the northern side, which flattens to nearly 16–20° in the southern fringe. We find an excellent correlation of the volcanic distribution with the varying slab dips. The high-angle slab dip segment has a relatively focused distribution of volcanic spots along a trench parallel narrow linear trend (Figure 11a, (X)). This observation is consistent with the experimental models for slab dip >30°, showing Mode 2 plumes (Figures 4c and 4d). The low-angle dip segment of the trench displays distributed volcanic spots scattered in the slab dip direction (Figure 11a, (Y)), which again matches closely with the formation of Mode 1 plumes and their distributions in our experimental models with low slab dips (10–20°) (Figures 4a and 4b). We propose the switch over of scattered to focused distributions of arc volcanism in the Central American trench as a consequence of Mode 1 to 2 transition due to slab steepening, ~16° to ~45° from SW toward NE (Currie et al., 2002; Stubailo et al., 2012; Trumbull et al., 2006). The Java trench also delineates a spectacular arcuate chain of active volcanism, covering a large distance, nearly 4,000 km (Figure 11b). The trench has two segments, defined by Sumatra and Java islands in the overriding plate. These two islands are dotted with numerous volcanic spots but well organized to form a linear belt, trending more or less parallel to the trench. However, it is possible to recognize visually a difference in their distribution patterns. The Sumatra Island that lies on the NW flank of the trench localizes the volcanic spots along a trench parallel line running for about 1,750 km. Their trench normal scattering is virtually absent. On the other side, Java Island displays a scattered distribution of the volcanic spots. Available seismic sections reveal that the Indo-Asian plate subducts along the Java trench with varying slab dips, that is, high-angle slab dip (~60°) beneath the Sumatra Island (Figure 11b, (X)) and relatively low-angle slab dip (~20°) beneath some portion of the Java Island (Figure 11b, (Y)). The present study suggests that the high-angle slab condition favored the plume processes to occur in Mode 2, which caused focusing of the volcanic spots along a trench parallel linear trend in the Sumatra segment with an average spacing of 46 to 54 km (Figure 11b), which is consistent with the experimental longitudinal spacing (~35–70 km). Flattening of slab dips resulted in a Mode 2 to 1 transition, giving rise to a scattered distribution of the volcanic spots in the Java Island. However, the degree of scattering is not as strong as in the case of Andes flat segments discussed above. We interpret such weak scattering in the Java Island as a direct consequence of a sharp change in the slab dip (20° to 40°) with increasing depth. The steeper slab segment promotes advection of partial melt up the slab and forced plumes to form a cluster. The stretch along which the slab dip sharply steepens limits the range of trench perpendicular scattering in the direction of slab dip (Chiu et al., 1991; Hall & Spakman, 2015).

Figure 11

Present-day volcanic spot distributions in (a) the Trans-Mexico Volcanic Belt (after Currie et al., 2002) and (b) the Java-Sumatra trench (Hall & Spakman, 2015). Locations of active volcanoes are shown as yellow triangles. The corresponding trench perpendicular sections (right side) show lateral variations of their subducting slab dips and associated arc volcanism patterns.

4.4 Timescale of Episodic Magmatic Events

Geological evidence suggests that most of the subduction zones witness episodic arc volcanism, with the timescale of periodicity ranging from tens of years to millions of years. Short-timescale periodicity is interpreted as a proxy to fluctuations in the magma chamber dynamics (Gerya et al., 2004). Understanding the mechanisms of long-timescale periodicity poses a major challenge in geodynamic studies. Recent measurements have also predicted 20–100 kyr to 0.3–1 Ma cycles of the eruption from tephra deposits in Pacific volcanic arcs (Gudmundsson, 1986; Kutterolf et al., 2013; Schindlbeck et al., 2018). The present investigation suggests the pulsating plume dynamics as a possible mechanism of such kiloyear frequency in arc volcanisms, reported from various subduction zones (Conder et al., 2002; Marsh, 1979; Tamura et al., 2002). In our experiments, the unsteady growth of plumes involved episodic partial melt supply into the overriding plate (supporting information Figure S6). For low slab dips (α < 30°), the melt-rich domes produced thereby do not grow simultaneously to form plumes; rather, they are episodically activated. We have calculated the time intervals of volcanic events from a single volcanic spot and compared them with the upscaled values obtained from our experimental and numerical model results. It is worth mentioning that the frequency found from our experimental findings is bimodal with one peak at 20–30 kyr owing to small fluctuations in material influx within a single plume and another peak at 300 kyr (Figure 8d), which can be attributed to a deficit of source material at the plume base. Our numerical model produces a similar 270- to 500-kyr frequency (Figure 8d) but not the 20-kyr frequency due to the model resolution, which likely failed to capture small-scale fluctuations within a single plume. Overall, our model results match with the timescales (200 to 400 kyr) of the frequency of natural volcanism (Figure 8d).

For high-angle slab dips (α > 30°), Mode 2 plumes evolve in a pulsating manner as the trailing domes sequentially meet their roots and accelerate the material supply through the plume tails (supporting information Figure S6). Our estimates for time-dependent supply of partially molten materials indicate an episodic material flux on a timescale of 300–500 kyr, which may help explain the timescale of frequency in arc volcanism. For example, Prueher and Rea (2001) have reported from the Kamchatka-Kurile arcs episodic explosive volcanism at an average time interval of ~0.5 Ma (Prueher & Rea, 2001). Based on this match, we suggest that pulsating plume dynamics plays a crucial role in dictating the episodic behavior of arc volcanism in subduction settings.

4.5 Limitations

We have adopted a mechanical modeling approach to develop our laboratory experiments and numerical simulations, excluding the possible effects of depth-dependent thermal and rheological changes. Thermomechanical modeling of subduction zones suggests that the complex thermal structures due to dehydration melting, coupled with strong temperature-dependent rheologies, give rise to heterogeneity in the system. Such heterogeneities might eventually act as an additional factor in triggering subsidiary plume generations in the mantle wedge. Our models are, however, simplified to show the effect of slab dip on the growth of cold plumes in the partially molten layer initiated by RTIs. Second, recent subduction models took into account compaction pressure to show partial melt focusing in the mantle wedge through porous media flows (Wilson et al., 2014). According to these models, varying bulk viscosity and permeability can largely control the direction of partial melt migration and thereby determine the location for partial melt focusing. Our models exclude the role of such porosity driven partial melt advection, which is expected to play an important role in plume-driven upward advection of partially molten materials. Moreover, the mantle wedge flow is not considered in this experimental study, assuming that plumes ascend through a vigorously stirred wedge. In our numerical simulations the corner flow initiated by subducting plate motion (3 cm/year) was too slow to affect the updrift or plume growth velocity. There is a need to fully explore how the wedge flow can influence the mode of plume generation on a wide spectrum of subduction kinematics. Mechanical mixing of partial melts originated at different depths during their updip advection is another potential factor to introduce complexity in plume dynamics. The present model has been simplified considering the partially molten zone as a single mechanical layer. The 3-D models presented in this study were run for a limited time span (<10 Ma), and they depict only the initiation of three-dimensional wave instabilities in the source layer. However, Zhu et al. (2009) ran 3-D simulations on a long timescale (~35 Ma) to demonstrate the evolution of complex 3-D instability geometry as a function of the viscosity of partially molten zone, which was varied between 10¹⁸ and 10²⁰ Pa s. Their models produced no finger-like plumes when the viscosity of the source layer was high (10²⁰ Pa s). We performed numerical simulations mostly with 2-D models because of our computational limitations.

Our laboratory models do not account for the probable effects of the lithospheric upper plate on plume distributions. Thermal variations at the lithosphere-asthenosphere boundary can generate heterogeneities in the upper plate, which can influence the melt pathways at shallow depths, leading to higher-order variations in the plume distribution. However, the overall first-order distribution of plumes would be controlled mainly by the slab dip, as demonstrated from our CFD models.

Despite all these limitations, our simple analog experiments and numerical models provide an insight into the role of slab dip in determining the distributions of volcanic centers in the overriding plates observed in the major subduction zones.

5 Conclusions

This study provides a synthesis of scaled laboratory experiments and CFD simulations to explain the origin of contrasting arc volcanisms in subduction zones, where the cold plumes are initiated by RTIs in the buoyant partially molten layer atop the dipping slabs. The slab dip (α) is found to play a key role in determining the modes of plume growth, leading to either a focused (linear) or a scattered (areal) distribution of the arc volcanoes. Dipping slabs develop two distinct sets of trench perpendicular and trench parallel RTI waves in the partially molten layers: longitudinal waves (λ_L) directed along the slab dip and transverse waves (λ_T) along the slab strike. For low slab dips (α < 30°), the λ_T/λ_L interference is the dominant mechanism in controlling the plume dynamics. Slab dips, exceeding a threshold value (α* ~ 30°), dampen the λ_T wave growth and promote the λ_L waves to capture the plume dynamics. We identify two principal modes of plume growth. In Mode 1, they initiate from melt-rich domes produced by λ_T/λ_L interference and grow randomly to form plumes distributed throughout the source layer, as observed in many subduction settings, for example, the Mexico subduction system. On the other hand, Mode 2 plumes localize at the upper fringe of a partially molten layer above the subducting slab, and they are mostly controlled by λ_L-driven advection of buoyant materials in the updip direction. Unlike Mode 1 plumes, they grow spontaneously with a regular spacing (~35–70 km) to form a trench parallel array, resembling the linear trench parallel volcanic arcs in many subduction zones, such as the Caribbean subduction zone. Our study underscores the role of α in governing the Mode 1 versus Mode 2 plume growth; the steepening of α results in a Mode 1 to 2 transitions at a threshold value (~30°). We propose that the migration of the arc magmatism through time reflects changes in slab dip (α). Thickness (T_s) of the partially molten zone is another factor in plume dynamics. Increasing T_s facilitates partial melt advection along slab dip, which in turn accelerates the upward drift of vertically growing melt-rich domes. This mechanism eventually gives rise to plume clusters in the updip slab region. Based on our model estimates, we predict a ~200- to 500-kyr periodicity of plume pulses, which explains the periodic nature of arc volcanism in subduction zone settings.

Acknowledgments

We thank three anonymous reviewers for their critical reviews and insightful suggestions for the improvement of our work. We also thank the Associate Editor and Editors Michael Bostock and Uri ten Brink who provided us constructive guidelines in revising the manuscript in various stages. Our study has greatly benefitted from their excellent reviews. We are grateful to Simon Gatehouse and Sanjib Banerjee, BHP, Australia, who helped us in refining the English language of our manuscript. This work has been supported by the DST-Science and Engineering Research Board (SERB), India, through J. C. Bose fellowship (SR/S2/JCB-36/2012) to N. M. and an Early Career Research project (ECR/2016/002045) granted by Science and Engineering Research Board (SERB), India, to A. B., UGC Junior Research Fellowship to D. G., and CSIR Senior Research Fellowship to G. M. We thank Anirban Das and Puspendu Saha for their constant help in the laboratory experiments.

Open Research

Data Availability Statement

The relevant data supporting the conclusions are present at FigShare (https://doi.org/10.6084/m9.figshare.c.5056610).