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Cold Plumes Initiated by Rayleigh‐Taylor Instabilities
in Subduction Zones, and Their Characteristic
Volcanic Distributions: The Role of Slab Dip
Dip Ghosh
1
, Giridas Maiti
1
, Nibir Mandal
1
, and Amiya Baruah
2
1
Department of Geological Sciences, Jadavpur University, Kolkata, India,
2
Department of Geology, Cotton University,
Guwahati, India
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 αexceeds a threshold value
(α*¼30°). 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.
1. Introduction
Understanding the underlying mechanisms of subduction‐driven arc volcanism has recently set a new mile-
stone 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 char-
acterized by approximately regularly spaced volcanoes along a trench parallel linear zone (called linear dis-
tribution 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 dis-
tribution pattern forms a laterally persistent narrow belt (~10 km wide; Marsh, 1979), also referred to as vol-
canic 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 distri-
butions in the overriding plate remain a challenging topic of research in the subduction geodynamics com-
munity (Grove et al., 2009, 2012).
It is now widely accepted that dehydration slab melting is the key process to drive arc volcanisms in subduc-
tion 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 over-
lying 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% H
2
Oin
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 Al
2
O
3
content can host 6 to 7 wt% chlorite
©2020. American Geophysical Union.
All Rights Reserved.
RESEARCH ARTICLE
10.1029/2020JB019814
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
Supporting Information:
•Supporting Information S1
Correspondence to:
N. Mandal,
nibir.mandal@jadavpuruniversity.in
Citation:
Ghosh, D., Maiti, G., Mandal, N., &
Baruah, A. (2020). Cold Plumes
Initiated by Rayleigh‐Taylor
Instabilities in Subduction Zones, and
their Characteristic Volcanic
Distributions: The Role of Slab Dip.
Journal of Geophysical Research: Solid
Earth,125, e2020JB019814. https://doi.
org/10.1029/2020JB019814
Received 25 MAR 2020
Accepted 22 JUL 2020
Accepted article online 24 JUL 2020
GHOSH ET AL. 1of23
that equates to 2 wt% bulk H
2
O at the P‐Tcondition 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
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* ¼t/t
T
(t
T
is the total runtime; new instabilities almost ceased to occur in the source layer after t
T
); Stage I: t* ¼0–0.2,
Stage II: t* ¼0.2–0.6, and Stage III: t* > 0.6.
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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 sedi-
ment signatures in arc volcanoes (Marschall & Schumacher, 2012; Zhang et al., 2020).
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 sub-
ducting 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, indi-
cate 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 den-
sity 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) phe-
nomenon, 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 perpen-
dicular 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 (10
18
–10
19
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 (10
20
–10
21
Pa s).
Despite significant progress in modeling subduction‐related cold plumes, there is a lack of systematic inves-
tigation 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 evo-
lution 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
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experiments to demonstrate the effects of αand support the experi-
mental 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 sys-
tem 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 (ρ¼ρ
o
/ρ
s
) and viscosities (R¼μ
o
/μ
s
); sub-
scripts oand srefer to the overburden and source layer, which repre-
sent 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
ρ¼1.03 and R¼10
−5
, while the second series had ρ¼1.13 and R¼25. All the parameters used in the
experiments are summarized in Table 1a. For models with R¼10
−5
(called R< 1 type model), we used
Polydimethylsiloxane (PDMS) (ρ
s
¼965 kg/m
3
and μ
s
¼10
2
Pa s), which agrees with the scaled down visc-
osity (in the order of 10
2
Pa s) of natural partially molten zones (~10
18
Pa s). We chose water (ρ
o
¼998 kg/m
3
and μ
o
¼10
−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.
The experimental setup consisted of a rectangular (60 cm × 30 cm × 30 cm) glass box (Figure S1 in the sup-
porting 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 mechani-
cally 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 R¼25 (referred to as R>1 type here-
after). These models consisted of source layers of hydraulic oil (ρ
s
¼970 kg/m
3
and μ
s
¼10 Pa s) and an over-
burden of translucent glue (ρ
ο
¼1,100 kg/m
3
and μ
o
¼250 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 kine-
matic 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
Table 1a
Model Dimensions and Material Properties Used in the Laboratory Experiments
Model parameters Symbol Units Value
R<1
Model length Lcm 60
Model width Wcm 30
Model height Hcm 30
Overburden density ρ
o
kg/m
3
998
Overburden viscosity μ
o
Pa s 10
−3
Source density ρ
s
kg/m
3
965
Source viscosity μ
s
Pa s 100
Viscosity ratio R—10
−5
Overburden density ρ
o
kg/m
3
1,100
Overburden viscosity μ
o
Pa s 250
R>1
Source density ρ
s
kg/m
3
970
Source viscosity μ
s
Pa s 10
Viscosity ratio R—25
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GHOSH ET AL. 4of23
et al., 2011). Accounting the model dimension ratio, this yields the strain rates ratio, ε*¼10
10
. Taking time as
reciprocal to strain rate, we obtain the time ratio in our model: τ¼10
−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 τindependently, without violating the dynamic similarity.
For our model, the dynamic scaling must satisfy a specific viscosity ratio, given by
μ*¼ρ*Λτ(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 ~10
18
Pa s (Zhu et al., 2009), the scaling factor yields the model mate-
rial viscosity as ~10
2
Pa s, which is the viscosity of PDMS used for the layer in our model.
For experiments with R¼25, we use the same length‐scale ratio (Λ) and similar density ratio (ρ*) factor but
have the timescale lower by 1 order (i.e., τ¼10
−11
) (supporting information Table S2). This leads to a visc-
osity 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 R¼10
2
, the overburden viscosity should be 10
3
. We chose translucent
glue (μ
o
¼250 Pa s) as the overburden to obtain the scaling factor closest to our desired value (~10
3
).
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 R¼10
−5
,αwas systematically varied
between 10° and 60° at an interval of 10°. For a given α, we chose T
s
¼0.5, 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 sec-
ond series of experiments with R¼25, αwas varied in the range 10° to 40° at an interval of 10° with T
s
¼0.5,
1 cm (Table S3).
Figure 2. Laboratory reference models with R¼10
−5
and T
s
¼0.5 cm showing the evolution of (a) Mode 1 plumes for
α¼20° and (b) Mode 2 plumes for α¼40°.
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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 instabil-
ities 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 conse-
quently 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 para-
meters 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 pro-
vide 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 normal-
ized experimental runtime (t* ¼t/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* ¼0–0.2): 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* ¼0.2–0.6): λ
T
and λ
L
waves progressively interfered to form 3‐D instability structures, char-
acterized 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 (α¼20°, T
s
¼0.5 cm, and R¼10
−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
~6kmand
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, k*
Tfrom 0.73 to 0.42, whereas k*
Lfrom 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 struc-
tures ultimately preserved a smaller number of large elongate domes (15 × 11 km) with transverse and long-
itudinal 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.
2.6. Reference Model—Mode 2
We present another reference model (α¼40°, T
s
¼0.5 cm, and R¼10
−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 advec-
tion of the buoyant fluid. Updip advection reduced the wave coalescence, reflecting much smaller variations
of the longitudinal wave number (k*
Lfrom 0.94 to 0.8) (Figure 3b, magenta line), but prompted RTIs to loca-
lize 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
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GHOSH ET AL. 6of23
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 (R¼10
−5
) for α¼10° to 40° to show how and
at what threshold αvalues (i.e., α*) the Mode 1 to Mode 2 transition occurs. At α¼10°, RTIs developed
plumes in Mode 1 (Figure 4a) (Stages I and II), where λ
T
>λ
L
(λ
T
/λ
L
¼1.2–2) (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 coales-
cence reduced their spatial density in the source layer as revealed by significant decrease in the wave numbers
k*
T(0.62 to 0.37) and k*
L(0.71 to 0.54), respectively (Figures 3a and 3b, black lines). In Stage III the model pro-
duced 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.
Figure 3. Experimental models showing (a) variations of normalized transverse wave numbers (k*
T) with normalized experimental run time (t*) for varying slab
dips (α). (b) Variation of normalized longitudinal wave numbers (k*
L) with t* for different values of α, where wave number k¼2π/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.
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Increasing αresulted in quantitative changes in the RTI structure (Figure 4b). For α¼20°,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 sig-
nificantly weaker; the wave numbers thus underwent relatively less changes (k*
T: 0.73 to 0.42 and k*
L: 0.86 to
0.64) in Stage II, as compared to the α¼10° 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 longitu-
dinal distances of 60–95 and 40–50 km, respectively (Figure 3e). Compared to plumes in the α¼10° model,
they ascended at much higher rates (13–16 cm/year) (Figure 3d).
Further increase in αto 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 ver-
tically as the λ
T
waves ceased to amplify with time; they rather updrifted at high velocities (10–12 cm/year)
Figure 4. Development of RTIs in analog experiments with R¼10
−5
for varying slab dips (α¼10–40°) and a constant
source layer thickness (T
s
¼0.5 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.
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(Figure 3d). The wave numbers, in longitudinal and transverse directions went through small changes; k*
T:
0:79 to 0.49 and k*
L: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 k*
Tremained 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., α¼20°). For a
small thickness (T
s
¼0.5 cm), the model developed globally both λ
L
and λ
T
wave instabilities, which inter-
fered 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 elon-
gate ridges, plunging down the slab dip (Figure S4a). Increase in T
s
(T
s
¼1.5 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 con-
tinuously 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 subduc-
tion setting, we used the R> 1 type of model and found qualitatively similar results. To demonstrate this, we
present here two specific models with R¼25 for low (α¼20°) and high (α¼30°) angle slab dips. For
α¼20°, 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 α¼30°, the RTI produced a dominant set of λ
L
waves, as in R< 1 mod-
els. 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
Figure 5. Development of Mode 1 and Mode 2 plumes for low‐angle and high‐angle slab dips analog experiments with
R¼25 and T
s
¼0.5 cm. The value of λ
T
typically varies from 10 to 60 km.
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contrast to rounded plume heads in case of R< 1. However, the
threshold value for Mode 1 to 2 transition (α*) remains unchanged.
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 simula-
tions: (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 find-
ings. The models had a horizontal dimension of 60 cm and a vertical dimension of 30 cm, chosen to repro-
duce the laboratory model dimensions. We performed laboratory‐scale model simulations for both R< 1 and
R> 1 with α¼20° and 30° and T
s
¼1 cm (model parameters given in Tables 1a and 1b).
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 zdimension (~200 km) parallel to
the trench. These models contained a low‐viscosity (10
17
Pa s) and low‐density (3,000 kg/m
3
) 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 infor-
mation 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 num-
ber (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(R¼10
−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 tran-
sition at α*¼30° 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 α¼20°, which increased to 1.2 cm/min (20 cm/year) when
α¼30° (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(R¼25) also showed Mode 1 to 2 transi-
tion 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
α¼10° to 40° keeping T
s
¼4 km, R¼10
2
, and Δρ¼300 kg/m
3
(Table S4). For α¼10°, 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
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 2–650–300
Subduction angle (α) (deg) 10–40 —
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plumes show little or no updrift as they attain a mature stage. Models with α¼20° produce similar Mode 1
plumes (Figure 6b). However, steepening of αresults 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*¼30°, 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 α¼40°, 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 α¼40° (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
¼4 km) in subduction zones for α¼10–40° (a–d). It is
noteworthy that the transition from Mode 1 to Mode 2 as αreaches 30°, as observed in physical experiments (Figure 4).
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3.4. Parametric Analysis
We varied the density contrast (Δρ) between the overburden and the source layers from 200 to 500 kg/m
3
to
investigate the buoyancy effects on the mode of plume growth. The overall plume dynamics remains unaf-
fected by Δρ, and the Mode 1 to 2 transition occurs at the same threshold slab dip (α*¼30°). However, their
ascent rates significantly increase with increasing Δρ, for example, 12.5 to 21.5 cm/year from 200 to
500 kg/m
3
at α¼20° (Figure 7a).
We investigated the role of viscosity ratio Rin controlling the evolution of plumes. Increasing Rlowers their
ascent velocity, for example, ~18 cm/year for R¼10
3
, which decreases to 8.5 cm/year when R¼10
5
, when
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 αvalues, (d) slab dip for given plate velocity and nonuniform source layer thickness, and
(e) volume of partially molten material pulses as a function of αand run time.
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α¼20° (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 Rbelow 10
2
again reduces the ascent velocity, possibly due to higher
viscous resistance within the source layer. The plume ascent rate becomes maximum for R¼10
3
(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 α¼10°, the ascent rate of plumes is nearly 4 cm/year for T
s
¼2 km; the rate increases to
25 cm/year when T
s
¼6 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 progres-
sively 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 α¼20°, 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 αto 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 αoccurs 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
Figure 8. (a) Validation of the numerical (R¼10
2
and Δρ¼300 kg/m
3
) and experimental (R¼25) plume growth velocities with published data. (b) Comparison
of the areal density of plumes from analog experiments (R¼25 and T
s
¼0.5–1.0 cm) with that of volcanoes from different subduction zones. (c) Comparison of
longitudinal and transverse plume spacing from our analog (R¼25 and T
s
¼0.5–1.0 cm) and numerical experiments (R¼10
2
,T
s
¼2–6 km, and Δρ¼300 kg/m
3
)
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).
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for Mode 1 to Mode 2 transition. The plume growth velocity also remained unaffected, but their updrift velo-
city dropped from 15 to ~10 cm/year when α¼20° (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 α¼10°, the maximum V
H
in a single pulse is 1,310 km
3
, increasing
to 7,518 km
3
when α¼40°. However, V
H
does not significantly change with other parameters such as den-
sity 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 km
3
,
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 R¼25 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 α¼20°, 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).
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 spa-
tial density of volcanic spots, measured as the number of volcanic spots per 1,000 km
2
in important subduc-
tion 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 scat-
tered 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 R¼25 and T
s
¼0.5–1.0 cm using their plan view images. The upscaling of our
laboratory estimates yield a spatial density of 0.35–0.7 per 1,000 km
2
(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) reg-
ularly 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 vol-
canoes 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 R¼25 and T
s
¼0.5–1.0 cm) and numerical (for
R¼10
2
,T
s
¼2–6 km, and Δρ¼300 kg/m
3
) results. The longitudinal and transverse plume spacing in labora-
tory 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 longi-
tudinal 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 con-
vergent 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
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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 mod-
eling, we thus consider αas the principal model parameter to explore how low‐angle versus high‐angle sub-
duction 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 sub-
duction 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 geome-
trical relation, αmust 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 αdue 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
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.
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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
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).
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important petrological factors in controlling T
s
are (1) the volume of H
2
O‐rich fluids released from the sub-
ducting 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
1field 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).
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 lat-
erally varying slab dips along the N‐S trending trench on the western margin of the South American over-
riding 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 seg-
ments 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 seg-
ments. 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 sub-
duction (>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 ran-
domly in space and time, which are in agreement with the scattered age distribution of volcanic spots in the
Pampean segment.
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
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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 dis-
tributions. 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 excel-
lent 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 pro-
pose 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 seg-
ments, 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
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 varia-
tions of their subducting slab dips and associated arc volcanism patterns.
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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 sub-
ducts 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 experi-
mental 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).
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 inter-
preted 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 measure-
ments have also predicted 20–100 kyr to 0.3–1 Ma cycles of the eruption from tephra deposits in Pacific vol-
canic 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 volcan-
isms, 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 cap-
ture 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 infor-
mation Figure S6). Our estimates for time‐dependent supply of partially molten materials indicate an episo-
dic 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 vol-
canism in subduction settings.
4.5. Limitations
We have adopted a mechanical modeling approach to develop our laboratory experiments and numer-
ical 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 subduc-
tion models took into account compaction pressure to show partial melt focusing in the mantle wedge
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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 loca-
tion for partial melt focusing. Our models exclude the role of such porosity driven partial melt advec-
tion, 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, assum-
ing 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 sin-
gle 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 evolu-
tion of complex 3‐D instability geometry as a function of the viscosity of partially molten zone, which
was varied between 10
18
and 10
20
Pa s. Their models produced no finger‐like plumes when the viscosity
of the source layer was high (10
20
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 dis-
tributions. 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 buoy-
ant 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 pro-
mote 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 mol-
ten layer above the subducting slab, and they are mostly controlled by λ
L
‐driven advection of buoyant mate-
rials 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 subduc-
tion zones, such as the Caribbean subduction zone. Our study underscores the role of αin governing the
Mode 1 versus Mode 2 plume growth; the steepening of αresults 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.
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Data Availability Statement
The relevant data supporting the conclusions are present at FigShare (https://doi.org/10.6084/m9.figshare.
c.5056610).
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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 sup-
ported 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
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