 
Regional model

Global model
 

 
Nondimensional

Dimensional

Nondimensional

Dimensional
 

Parameter

Symbol

value

value

value

value

Units


Mantle depth

D

1

600

1

2890

km

Reference viscosity

η
_{0}

1

6.92×10^{27}

1

10^{23}

Pa s

Surface Ra number

R
a
_{
H,0}

0.1


  


Internal Ra number

R
a
_{
T,0}
  
10^{6}





FrankKamenetskii 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

6.34×10^{5}

Pa

Activation energy

E
_{act}
  
11.55

240

kJmol ^{−1}

Activation volume

V
_{act}
  
4.0

8.8878×10^{−7}

m ^{3}mol

Upper viscosity cutoff

η
_{max}

10^{2}
η
_{0}

6.92×10^{29}

10^{5}
η
_{0}

10^{28}

Pa s

Lower viscosity cutoff

η
_{min}

10^{−8}
η
_{0}

6.92×10^{19}

10^{−4}
η
_{0}

10^{19}

Pa s

Stickyair layer:
^{c}
 
Thickness

d
_{
st
}

0.05

30

0.05

145

km

Viscosity

η
_{
st
}

10^{−8}
η
_{0}

6.92×10^{19}

10^{−2}
η
_{0}

10^{21}

Pa s

Ccondition ^{d}

C
_{Stokes}

1.5×10^{−7}



0.175






^{a}Indicated is standard setup; parameter variation is mentioned separately

^{b}For actual values, see Tables 2 and 3

^{c}If applied

^{d}Indicates suitable freesurface approximation with stickyair approach if C
_{Stokes}≪1 (Crameri et al. 2012a)