Table 1 Parameters used in this study

Mantle depth

D

1

600

1

2890

km

Reference viscosity

η ₀

1

6.92×10²⁷

1

10²³

Pa s

Surface Ra number

R a _H,0

0.1

-

-

Internal Ra number

R a _T,0

10⁶

-

-

Frank-Kamenetskii parameter

θ

60

-

-

Stress exponent

n

1

-

-

Gravitational acceleration

g

-

9.81

-

9.81

ms ⁻²

Thermal conductivity

k

-

3

-

3

Wm ⁻¹ K ⁻¹

Thermal diffusivity

κ

1

10⁻⁶

1

10⁻⁶

m ² s ⁻¹

Thermal expansivity

α

-

3×10⁻⁵

-

3×10⁻⁵

K ⁻¹

Temperature gradient

Δ T

-

2500

-

2500

K

Reference density

ρ ₀

-

3300

-

3300

kg m ⁻³

Heat capacity

C p ₀

-

1200

-

1200

Jkg ⁻¹ K ⁻¹

Internal heating rate

H

1

6.31×10⁻¹²

20

5.44×10⁻¹²

Wkg ⁻¹

Constant yield stress

σ _y,const

variable ^b

variable ^b

variable ^b

variable ^b

MPa

Yield stress gradient

Δ σ _y

variable ^b

variable ^b

variable ^b

variable ^b

-

Friction coefficient

μ

0.09 ^a

-

-

Cohesion

C

100

6.34×10⁵

Pa

Activation energy

E _act

11.55

240

kJmol ⁻¹

Activation volume

V _act

4.0

8.8878×10⁻⁷

m ³mol

Upper viscosity cutoff

η _max

10² η ₀

6.92×10²⁹

10⁵ η ₀

10²⁸

Pa s

Lower viscosity cutoff

η _min

10⁻⁸ η ₀

6.92×10¹⁹

10⁻⁴ η ₀

10¹⁹

Pa s

Sticky-air layer: ^c

Thickness

d _st

0.05

30

0.05

145

km

Viscosity

η _st

10⁻⁸ η ₀

6.92×10¹⁹

10⁻² η ₀

10²¹

Pa s

C-condition ^d

C _Stokes

1.5×10⁻⁷

-

0.175

-

-