Table 2 Nomenclature and reference values

Reference temperature scale

\({T}_0\)

1 K = 1\(^\circ\)C

–

Surface temperature

\({T}^*_s\)

273 K = 0\(^\circ\)C

\({T}_{{\text{s}}}\)=0

Mantle temperature

\({T}^*_m\)

1623 K = 1350\(^\circ\)C

\({T}_{{\text{m}}}\)=1350

Surface heat flow \(^{c}\)

\(q^*_s\)

\(^{\S }\) W/m\(^2\)

\(q_s\) \(^{\S }\)

Reference density

\(\rho _0\)

3300 kg/m\(^3\)

–

Crustal density \(^{c}\)

\(\rho ^*_c\)

2750 kg/m\(^3\)

\(\rho _c\) = 0.833333

Mantle density

\(\rho ^*_m\)

3300 kg/m\(^3\)

\(\rho _m\) = 1

Reference thermal conductivity

\(k_0\)

3.1  W/(m K)

–

Crustal thermal conductivity \(^{c}\)

\(k^*_c\)

2.5  W/(m K)

\(k_c\) = 0.8064516

Mantle thermal conductivity

\(k^*_m\)

3.1  W/(m K)

\(k_m\) = 1

Volumetric heat production (upper crust) \(^{c}\)

\({H}^*_1\)

1.3 μW/m\(^3\)

\({H}_1\) = 0.419354

Volumetric heat production (lower crust) \(^{c}\)

\({H}_2^*\)

0.27 μW/m\(^3\)

\({H}_2\) = 0.087097

Age of overriding crust \(^{o}\)

\({A}_c^*\)

\(^{\S }\) Myr

\({A}_c\) \(^{\S }\)

Age of subduction \(^{t}\)

\({A}_s^*\)

\(^{\S }\) Myr

\({{A}_s}^{\S }\)

Age of subducting slab

\({A}^*\)

\(^{\S }\) Myr

\({A}^{\S }\)

Reference length scale

\(h_0\)

1 km

–

Depth of base of upper crust \(^{c}\)

\(z_1^*\)

15 km

\(z_1\) = 15

Depth of base of lower crust (Moho)

\(z_2^*\)

\(^{\S }\) km

\({z_2}^{\S }\)

Trench depth

\(z_\text {trench}^*\)

\(^{\S }\) km

\(z_\text {trench}^{\S }\)

Position of the coast line

\(x_\text {coast}^*\)

\(^{\S }\) km

\(x_\text {coast}^{\S }\)

Wedge inflow/outflow transition depth

\(z_\text {io}^*\)

\(^{\S }\) km

\(z_\text {io}^{\S }\)

Depth of domain

\({D}^*\)

\(^{\S }\) km

\({D}^{\S }\)

Width of domain

\({L}^*\)

\(^{\S }\) km

\({L}^{\S}\)

Depth of change from decoupling to coupling

\(d_c^*\)

80 km

\(d_c\) = 80

Reference heat capacity

\(c_{{{\text{p}}_0}}\)

1250 J/(kg K)

–

Reference thermal diffusivity

\(\kappa _0\)

0.7515\(\times\)10\(^{\text {-6}}\) m\(^2\)/s

–

Activation energy

E

540 kJ/mol

–

Power-law exponent

n

3.5

–

Pre-exponential constant

\({A}^*_\eta\)

28968.6 Pa s\(^{1/n}\)

–

Reference viscosity scale

\(\eta _0\)

10\(^{\text {21}}\) Pa s

–

Viscosity cap

\(\eta ^*_\text {max}\)

10\(^{\text {25}}\) Pa s

–

Gas constant

\({R}^*\)

8.3145 J/(mol K)

–

Derived velocity scale

\({v}_0\)

23.716014 mm/yr

–

Convergence velocity

\({V}_s^*\)

\(^{\S }\) mm/yr

\({{V}_s}^{\S }\)