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Table 1 Physical parameters

From: On the evolution of the water ocean in the plate-mantle system

Symbol Meaning Value
η 0 Reference viscosity 1021 (Pa s)
∆η Viscosity jump 30
ρ 0 Reference density 3300 (kg m−3)
∆ρ w Density anomalies due to mantle water content 4.125 (kg m−3)
g 0 Gravity 9.8 (m s−2)
α 0 Reference thermal expansivity 5 × 10−5 (K−1)
κ 0 Reference thermal diffusivity 7 × 10−7 (m2 s−1)
∆T sa Temperature scale 2500 (K)
T s Surface temperature 300 (K)
T CMB Temperature at the CMB 4000 (K)
C p Heat capacity 1250 (J kg−1 K−1)
L m Latent heat 6.25 × 105 (J kg−1)
H Internal heating rate 5.2 × 10−12 (W kg−1)
C Y Cohesion stress 10 (MPa)
E d Activation energy of dry mantle 290 (kJ mol−1)
V d Activation volume of dry mantle 2.4 × 10−6 (m3 mol−1)
E w Activation energy of wet mantle 380 (kJ mol−1)
V w Activation volume of wet mantle 4 × 10−6 (m3 mol−1)
R Gas constant 8.134 (J K−1 mol−1)
D Thickness of mantle 2890 (km)
  1. The Rayleigh number is computed as ρ0g0α0∆TsaD3/κ0η0~1.4 × 108 with values listed in Table 1. Activation energy and volume for dry mantle are taken from Yamazaki and Karato (2001) and for wet mantle are taken from Korenaga and Karato (2008). Results are not changed with rheological parameters taken from Karato and Wu (1993) for wet mantle. The latent heat shown here is used for temperature feedback caused by partial melting (Xie and Tackley 2004)