Regional model | Global model | |||||
---|---|---|---|---|---|---|
Non-dimensional | Dimensional | Non-dimensional | Dimensional | |||
Parameter | Symbol | value | value | value | value | Units |
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 | - | - |