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Generation and transport of liquidwater in the high-pressure icelayers of Ganymede and Titan
Klára Kalousová1, Christophe Sotin2
1 Department of Geophysics, Charles University, Prague2 Jet Propulsion Laboratory - California Institute of Technology, Pasadena
Ada Lovelace Workshop on Numerical Modellingof Mantle and Lithosphere Dynamics,
La Certosa di Pontignano, Italy,August 26, 2019
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Is there life somewhere else in the Universe?
How do we find it?
NASA: Follow the water
-
Is there life somewhere else in the Universe?
How do we find it?
NASA: Follow the water
-
Is there life somewhere else in the Universe?
How do we find it?
NASA: Follow the water
-
Follow the waterI life might have started at the bottom of Earth’s oceans
I water-rock interactions → rich communities of organismsI Galileo & Cassini: deep oceans within the icy moons → ocean worlds
I Europa:- induced magnetic field- geologic evidenceI Ganymede:- induced magnetic field- auroral ovals oscillationI Titan:- electric signal variations- large Love numberI Enceladus:- geysers- libration of outer layer
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Follow the waterI life might have started at the bottom of Earth’s oceansI water-rock interactions → rich communities of organisms
I Galileo & Cassini: deep oceans within the icy moons → ocean worlds
I Europa:- induced magnetic field- geologic evidenceI Ganymede:- induced magnetic field- auroral ovals oscillationI Titan:- electric signal variations- large Love numberI Enceladus:- geysers- libration of outer layer
-
Follow the waterI life might have started at the bottom of Earth’s oceansI water-rock interactions → rich communities of organismsI Galileo & Cassini: deep oceans within the icy moons → ocean worlds
I Europa:- induced magnetic field- geologic evidenceI Ganymede:- induced magnetic field- auroral ovals oscillationI Titan:- electric signal variations- large Love numberI Enceladus:- geysers- libration of outer layer
-
Follow the waterI life might have started at the bottom of Earth’s oceansI water-rock interactions → rich communities of organismsI Galileo & Cassini: deep oceans within the icy moons → ocean worlds
I Europa:- induced magnetic field- geologic evidence
I Ganymede:- induced magnetic field- auroral ovals oscillationI Titan:- electric signal variations- large Love numberI Enceladus:- geysers- libration of outer layer
-
Follow the waterI life might have started at the bottom of Earth’s oceansI water-rock interactions → rich communities of organismsI Galileo & Cassini: deep oceans within the icy moons → ocean worlds
I Europa:- induced magnetic field- geologic evidenceI Ganymede:- induced magnetic field- auroral ovals oscillation
I Titan:- electric signal variations- large Love numberI Enceladus:- geysers- libration of outer layer
-
Follow the waterI life might have started at the bottom of Earth’s oceansI water-rock interactions → rich communities of organismsI Galileo & Cassini: deep oceans within the icy moons → ocean worlds
I Europa:- induced magnetic field- geologic evidenceI Ganymede:- induced magnetic field- auroral ovals oscillationI Titan:- electric signal variations- large Love number
I Enceladus:- geysers- libration of outer layer
-
Follow the waterI life might have started at the bottom of Earth’s oceansI water-rock interactions → rich communities of organismsI Galileo & Cassini: deep oceans within the icy moons → ocean worlds
I Europa:- induced magnetic field- geologic evidenceI Ganymede:- induced magnetic field- auroral ovals oscillationI Titan:- electric signal variations- large Love numberI Enceladus:- geysers- libration of outer layer
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Europa & EnceladusI direct contact of silicates with
the oceanI conditions similar to the Earth
oceans - emergence of life?
Ganymede & TitanI thick HP ice layer between
silicates and the oceanI is water & material exchange
possible?
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Europa & EnceladusI direct contact of silicates with
the oceanI conditions similar to the Earth
oceans - emergence of life?
Ganymede & TitanI thick HP ice layer between
silicates and the oceanI is water & material exchange
possible?
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GanymedeI full differentiation:
MoI=0.310I tenuous O2 exosphereI intrinsic magnetic field
TitanI partial differentiation:
MoI=0.3414I dense N2-CH4-Ar atmosphere→ possibly ongoing exchange?
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GanymedeI full differentiation:
MoI=0.310I tenuous O2 exosphereI intrinsic magnetic field
TitanI partial differentiation:
MoI=0.3414I dense N2-CH4-Ar atmosphere→ possibly ongoing exchange?
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GanymedeI dehydrated mantle
+ thick H2O layerI H&400 km: only ice VI
TitanI core of hydrated silicates
+ thinner H2O layerI H∼50–300 km: ices VI, V, III?
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GanymedeI dehydrated mantle
+ thick H2O layerI H&400 km: only ice VI
TitanI core of hydrated silicates
+ thinner H2O layerI H∼50–300 km: ices VI, V, III?
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Heat and material exchange
I no direct contact between the silicates and the oceanI BUT: material exchange possible through convectionI HP ice dynamics governs heat extraction from the interior
I 1d thermo(chemical) evolution of the whole hydrosphere:e.g. Kirk & Stevenson (1987), Grasset & Sotin (1996), Showman &Malhotra (1997), Tobie + (2005), Fortes + (2007), Grindrod +(2008), Bland + (2009), Noack + (2016)
a) T=Tm, heat transfer through HP ice not treatedb) use of scaling laws based on the hot TBL instability
I effect of ice phases transitions on convection:a) linear stability analysis (Bercovici +, 1986; Sotin & Parmentier,1989)b) 2d convection in ice VI and VII mantle (Journaux & Noack, 2015)
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Heat and material exchange
I no direct contact between the silicates and the oceanI BUT: material exchange possible through convectionI HP ice dynamics governs heat extraction from the interior
I 1d thermo(chemical) evolution of the whole hydrosphere:e.g. Kirk & Stevenson (1987), Grasset & Sotin (1996), Showman &Malhotra (1997), Tobie + (2005), Fortes + (2007), Grindrod +(2008), Bland + (2009), Noack + (2016)
a) T=Tm, heat transfer through HP ice not treatedb) use of scaling laws based on the hot TBL instability
I effect of ice phases transitions on convection:a) linear stability analysis (Bercovici +, 1986; Sotin & Parmentier,1989)b) 2d convection in ice VI and VII mantle (Journaux & Noack, 2015)
-
Heat and material exchange
I no direct contact between the silicates and the oceanI BUT: material exchange possible through convectionI HP ice dynamics governs heat extraction from the interior
I 1d thermo(chemical) evolution of the whole hydrosphere:e.g. Kirk & Stevenson (1987), Grasset & Sotin (1996), Showman &Malhotra (1997), Tobie + (2005), Fortes + (2007), Grindrod +(2008), Bland + (2009), Noack + (2016)
a) T=Tm, heat transfer through HP ice not treatedb) use of scaling laws based on the hot TBL instability
I effect of ice phases transitions on convection:a) linear stability analysis (Bercovici +, 1986; Sotin & Parmentier,1989)b) 2d convection in ice VI and VII mantle (Journaux & Noack, 2015)
-
Heat and material exchange
I no direct contact between the silicates and the oceanI BUT: material exchange possible through convectionI HP ice dynamics governs heat extraction from the interior
I 1d thermo(chemical) evolution of the whole hydrosphere:e.g. Kirk & Stevenson (1987), Grasset & Sotin (1996), Showman &Malhotra (1997), Tobie + (2005), Fortes + (2007), Grindrod +(2008), Bland + (2009), Noack + (2016)
a) T=Tm, heat transfer through HP ice not treatedb) use of scaling laws based on the hot TBL instability
I effect of ice phases transitions on convection:a) linear stability analysis (Bercovici +, 1986; Sotin & Parmentier,1989)b) 2d convection in ice VI and VII mantle (Journaux & Noack, 2015)
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Heat and material exchange
I Choblet + (2017): solid-state thermal convection in 3d sphericalI Tmax and Tavrg > Tmelt in the upper part
→ cold thermal boundary layer cannot exist in a solid state→ two-phase mixture model (Bercovici +, 2001; Šrámek +, 2007)
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Heat and material exchange
I Choblet + (2017): solid-state thermal convection in 3d sphericalI Tmax and Tavrg > Tmelt in the upper part→ cold thermal boundary layer cannot exist in a solid state
→ two-phase mixture model (Bercovici +, 2001; Šrámek +, 2007)
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Heat and material exchange
I Choblet + (2017): solid-state thermal convection in 3d sphericalI Tmax and Tavrg > Tmelt in the upper part→ cold thermal boundary layer cannot exist in a solid state→ two-phase mixture model (Bercovici +, 2001; Šrámek +, 2007)
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Model setting
I pure H2O system (solid ice & liquid water):
a) TiTm: one-phase material (water only)
I porosity φ= VwVi+Vw (vol. fraction of water in the mixture)I amount of ice: 1−φ
I different material densities → 2 mass balancesI phase separation → 2 linear momentum balancesI thermal equilibrium between the two phases → 1 energy balance
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Model setting
I pure H2O system (solid ice & liquid water):
a) TiTm: one-phase material (water only)
I porosity φ= VwVi+Vw (vol. fraction of water in the mixture)I amount of ice: 1−φ
I different material densities → 2 mass balancesI phase separation → 2 linear momentum balancesI thermal equilibrium between the two phases → 1 energy balance
-
Model setting
I pure H2O system (solid ice & liquid water):
a) TiTm: one-phase material (water only)
I porosity φ= VwVi+Vw (vol. fraction of water in the mixture)I amount of ice: 1−φ
I different material densities → 2 mass balancesI phase separation → 2 linear momentum balancesI thermal equilibrium between the two phases → 1 energy balance
-
Model setting
I pure H2O system (solid ice & liquid water):
a) TiTm: one-phase material (water only)
I porosity φ= VwVi+Vw (vol. fraction of water in the mixture)I amount of ice: 1−φ
I different material densities → 2 mass balancesI phase separation → 2 linear momentum balancesI thermal equilibrium between the two phases → 1 energy balance
-
Model setting
I pure H2O system (solid ice & liquid water):
a) TiTm: one-phase material (water only)
I porosity φ= VwVi+Vw (vol. fraction of water in the mixture)I amount of ice: 1−φ
I different material densities → 2 mass balancesI phase separation → 2 linear momentum balancesI thermal equilibrium between the two phases → 1 energy balance
-
Model setting
I pure H2O system (solid ice & liquid water):
a) TiTm: one-phase material (water only)
I porosity φ= VwVi+Vw (vol. fraction of water in the mixture)I amount of ice: 1−φ
I different material densities → 2 mass balancesI phase separation → 2 linear momentum balancesI thermal equilibrium between the two phases → 1 energy balance
-
Model setting
I pure H2O system (solid ice & liquid water):
a) TiTm: one-phase material (water only)
I porosity φ= VwVi+Vw (vol. fraction of water in the mixture)I amount of ice: 1−φ
I different material densities → 2 mass balancesI phase separation → 2 linear momentum balancesI thermal equilibrium between the two phases → 1 energy balance
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Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation
2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of ice∇ · vi = 0
I linear momentum balance of ice0 = −∇Π− ρiαiTg +∇ · σi
I energy balance of ice
ρicpi∂T∂t
+ ρicpi vi · ∇T − ρiTαivi · g = ∇ · (ki∇T ) + σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw
3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρicpi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of ice∇ · vi = 0
I linear momentum balance of ice0 = −∇Π− ρiαiTg +∇ · σi
I energy balance of ice
ρicpi∂T∂t
+ ρicpi vi · ∇T − ρiTαivi · g = ∇ · (ki∇T ) + σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw
3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρicpi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · v = 0
I linear momentum balance of ice0 = −∇Π− ρiαiTg +∇ · σi
I energy balance of ice
ρicpi∂T∂t
+ ρicpi vi · ∇T − ρiTαivi · g = ∇ · (ki∇T ) + σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw
3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρicpi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · v = 0
I linear momentum balance of ice0 = −∇Π− ραTg +∇ · σ
I energy balance of ice
ρicpi∂T∂t
+ ρicpi vi · ∇T − ρiTαivi · g = ∇ · (ki∇T ) + σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw
3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρicpi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · v = 0
I linear momentum balance of ice0 = −∇Π− ραTg +∇ · σ
I energy balance of mixture
ρcp∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + σ : ∇v
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi
, Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρicpi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · v = 0
I linear momentum balance of ice0 = −∇Π− ραTg +∇ · σ
I energy balance of mixture
ρcp∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + σ : ∇v
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi
, Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρicpi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · v = 0
I linear momentum balance of ice0 = −∇Π− ραTg +∇ · (1−φ)σi
I energy balance of mixture
ρcp∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + (1−φ)σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi
, ρcp → (1−φ)ρicpi → ρicpi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · v = 0
I linear momentum balance of ice0 = −∇Π− ραTg +∇ · (1−φ)σi
I energy balance of mixture
ρcp∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + (1−φ)σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi
, ρcp → (1−φ)ρicpi → ρicpi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · v = 0
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi
I energy balance of mixture
ρcp∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + (1−φ)σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi
→ ρicpi4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ
→ latent heat Lm consumption/release ; solid phase change5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · v = 0
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi
I energy balance of mixture
ρcp∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + (1−φ)σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · v = 0
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi
I energy balance of mixture
ρcp∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + (1−φ)σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · v = 0
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi
I energy balance of mixture
ρicpi∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + (1−φ)σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing
→ compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · v = 0
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi
I energy balance of mixture
ρicpi∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + (1−φ)σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture
→ ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · v =
∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi
I energy balance of mixtureρic
pi∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + (1−φ)σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture
→ ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · vi +∇ · [φ(vw−vi)] =
∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi
I energy balance of mixtureρic
pi∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + (1−φ)σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0
→ ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · vi +∇ · [φ(vw−vi)] =
∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi
I energy balance of mixtureρic
pi∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + (1−φ)σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ
→ latent heat Lm consumption/release ; solid phase change5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · vi +∇ · [φ(vw−vi)] =
∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi
I energy balance of mixtureρic
pi∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + (1−φ)σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ
→ latent heat Lm consumption/release ; solid phase change5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · vi +∇ · [φ(vw−vi)] =
∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi +∇
[(1−φ)µi
φ(∇ · vi)
]I energy balance of mixture
ρicpi∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + (1−φ)σi : ∇vi
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ
→ latent heat Lm consumption/release ; solid phase change5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · vi +∇ · [φ(vw−vi)] =
∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi +∇
[(1−φ)µi
φ(∇ · vi)
]I energy balance of mixtureρic
pi∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + (1−φ)σi : ∇vi +1− φφ
µi(∇ · vi)2
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ
→ latent heat Lm consumption/release ; solid phase change5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · vi +∇ · [φ(vw−vi)] =
∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi +∇
[(1−φ)µi
φ(∇ · vi)
]I energy balance of mixture (Ψ̃ = (1−φ)σi:∇vi+ 1−φφ µi(∇·vi)2)
ρicpi∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + Ψ̃
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release
; solid phase change5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · vi +∇ · [φ(vw−vi)] =
∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi +∇
[(1−φ)µi
φ(∇ · vi)
]I energy balance of mixture (Ψ̃ = (1−φ)σi:∇vi+ 1−φφ µi(∇·vi)2)
ρicpi∂T∂t
+ ρcpv · ∇T − ρiTαv · g = ∇ · (k∇T ) + Ψ̃
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release
; solid phase change5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · vi +∇ · [φ(vw−vi)] =
∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi +∇
[(1−φ)µi
φ(∇ · vi)
]I energy balance of mixture (Ψ̃ = (1−φ)σi:∇vi+ 1−φφ µi(∇·vi)2)
ρicpi∂T∂t
+ ρcpv · ∇T − ρiTαv · g + Γm Lm = ∇ · (k∇T ) + Ψ̃
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through ice
I mass balance of mixture∇ · vi +∇ · [φ(vw−vi)] =
∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi +∇
[(1−φ)µi
φ(∇ · vi)
]I energy balance of mixture (Ψ̃ = (1−φ)σi:∇vi+ 1−φφ µi(∇·vi)2)
ρicpi∂T∂t
+ ρcpv · ∇T − ρiTαv · g + Γm Lm + Γs Ls = ∇ · (k∇T ) + Ψ̃
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0
→ water percolation through ice
I mass balance of mixture∇ · vi +∇ · [φ(vw−vi)] =
∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg +∇ · (1−φ)σi +∇
[(1−φ)µi
φ(∇ · vi)
]I energy balance of mixture (Ψ̃ = (1−φ)σi:∇vi+ 1−φφ µi(∇·vi)2)
ρicpi∂T∂t
+ ρcpv · ∇T − ρiTαv · g + Γm Lm + Γs Ls = ∇ · (k∇T ) + Ψ̃
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0
→ water percolation through ice
I mass balance of mixture∇ · vi +∇ · [φ(vw−vi)] =
∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg − φ∆ρg +∇ · (1−φ)σi +∇
[(1−φ)µi
φ(∇ · vi)
]I energy balance of mixture (Ψ̃ = (1−φ)σi:∇vi+ 1−φφ µi(∇·vi)2)
ρicpi∂T∂t
+ ρcpv · ∇T − ρiTαv · g + Γm Lm + Γs Ls = ∇ · (k∇T ) + Ψ̃
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through iceI mass balance of mixture
∇ · vi +∇ · [φ(vw−vi)] =∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg − φ∆ρg +∇ · (1−φ)σi +∇
[(1−φ)µi
φ(∇ · vi)
]I energy balance of mixture (Ψ̃ = (1−φ)σi:∇vi+ 1−φφ µi(∇·vi)2)
ρicpi∂T∂t
+ ρcpv · ∇T − ρiTαv · g + Γm Lm + Γs Ls = ∇ · (k∇T ) + Ψ̃
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through iceI mass balance of mixture
∇ · vi +∇ · [φ(vw−vi)] =∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg − φ∆ρg +∇ · (1−φ)σi +∇
[(1−φ)µi
φ(∇ · vi)
]I energy balance of mixture (Ψ = (1−φ)σi:∇vi+ 1−φφ µi(∇·vi)2+
µwφ2Kφ
(vw−vi)2)
ρicpi∂T∂t
+ ρcpv · ∇T − ρiTαv · g + Γm Lm + Γs Ls = ∇ · (k∇T ) + Ψ
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Governing equations1. Thermal convection in ice - incompressible extended Boussinesq approximation2. Mixture of two incompressible components: ξi → ξ := (1−φ)ξi + φξw3. µw�µi: σ → (1−φ)σi , Tw=Tm: ρα→ (1−φ)ρiαi , ρcp → (1−φ)ρicpi → ρic
pi
4. Melting/freezing → compressible mixture → ∇ · vi 6= 0 → ζi∼µiφ→ latent heat Lm consumption/release ; solid phase change
5. Melt buoyancy: ∆ρ=ρi−ρw 6= 0 → water percolation through iceI mass balance of mixture
∇ · vi +∇ · [φ(vw−vi)] =∆ρ
ρiρwΓm
I linear momentum balance of ice0 = −∇Π− (1−φ)ρiαiTg − φ∆ρg +∇ · (1−φ)σi +∇
[(1−φ)µi
φ(∇ · vi)
]I energy balance of mixture (Ψ = (1−φ)σi:∇vi+ 1−φφ µi(∇·vi)2+
µwφ2Kφ
(vw−vi)2)
ρicpi∂T∂t
+ ρcpv · ∇T − ρiTαv · g + Γm Lm + Γs Ls = ∇ · (k∇T ) + Ψ
I linear momentum balance of water ∼ Darcy lawvw − vi = −
Kφµwφ
(1−φ)∆ρg
I mass balance of water → advection of porosity∂φ
∂t+∇ · (φvw) =
Γm
ρw
-
Material parametersI ice permeable to water transport above a threshold porosity φc
Kφ ={
k0(φ−φc)2 φ ≥ φc0 φ < φc
I temperature and depth dependent ice viscosity
µi = µ0 exp[
QR
(1T−
1Tm(z)
)]
-
Implementation
I FEniCS (fenicsproject.org, Logg +, 2012; Alnaes +, 2015), MPI
-
Reference simulation for Ganymede
H=200 km, µi=1015 Pa s, qs=20 mW m−2
I silicates: T=Tm, φ∼few %: volatiles leachingI interior: T av
-
Reference simulation for Ganymede
H=200 km, µi=1015 Pa s, qs=20 mW m−2
I silicates: T=Tm, φ∼few %: volatiles leachingI interior: T av
-
Reference simulation for Ganymede
H=200 km, µi=1015 Pa s, qs=20 mW m−2
I silicates: T=Tm, φ∼few %: volatiles leaching
I interior: T av
-
Reference simulation for Ganymede
H=200 km, µi=1015 Pa s, qs=20 mW m−2
I silicates: T=Tm, φ∼few %: volatiles leachingI interior: T av
-
Reference simulation for Ganymede
H=200 km, µi=1015 Pa s, qs=20 mW m−2
I silicates: T=Tm, φ∼few %: volatiles leachingI interior: T av
-
Increasing HP ice layer thickness H (∼ increasing Ra)
-
Increasing HP ice layer thickness H (∼ increasing Ra)
(1) Direct exchange ∼ small Rayleigh number
-
Increasing HP ice layer thickness H (∼ increasing Ra)
(1) Direct exchange ∼ small Rayleigh number
(2) Indirect exchange ∼ medium Rayleigh number
-
Increasing HP ice layer thickness H (∼ increasing Ra)
(1) Direct exchange ∼ small Rayleigh number
(2) Indirect exchange ∼ medium Rayleigh number
(3) Limited exchange ∼ medium Rayleigh number
-
Increasing HP ice layer thickness H (∼ increasing Ra)
(1) Direct exchange ∼ small Rayleigh number
(2) Indirect exchange ∼ medium Rayleigh number
(3) Limited exchange ∼ medium Rayleigh number
(4) No exchange ∼ large Rayleigh number
-
Results of parametric study
I degree of exchange decreases withI increasing ice layer thickness H (∼ time)
I decreasing ice viscosity µiI decreasing heat flux from silicates qs
-
Results of parametric study
I degree of exchange decreases withI increasing ice layer thickness H (∼ time)I decreasing ice viscosity µi
I decreasing heat flux from silicates qs
-
Results of parametric study
I degree of exchange decreases withI increasing ice layer thickness H (∼ time)I decreasing ice viscosity µiI decreasing heat flux from silicates qs
-
Long-term evolution modeling
I 2d model: strong dependence on input parameters:- HP ice layer thickness H- ice viscosity µi- silicates heat flux qs
I 1d thermo(-chemical) evolution model:- scaling laws for rocky interior, HP ice layer, ocean, ice I crust- qs and H are part of solution- µi remains an input parameter
-
Long-term evolution modeling
I 2d model: strong dependence on input parameters:- HP ice layer thickness H- ice viscosity µi- silicates heat flux qs
I 1d thermo(-chemical) evolution model:- scaling laws for rocky interior, HP ice layer, ocean, ice I crust- qs and H are part of solution- µi remains an input parameter
-
Critical heat flux for bottom melting
I fixed viscosity µi, range of qs and H
→ critical qcs for bottom melting: qcs = αH − β
-
Critical heat flux for bottom melting
I fixed viscosity µi, range of qs and H
→ critical qcs for bottom melting: qcs = αH − β
-
Critical heat flux for bottom melting
I fixed viscosity µi, range of qs and H
→ critical qcs for bottom melting: qcs = αH − β
-
Critical heat flux for bottom melting
I fixed viscosity µi, range of qs and H
→ critical qcs for bottom melting: qcs = αH − β
-
Present-day bottom melting: Ganymede vs TitanI Titan, µi = 1015 Pa s: qcs ∝ H
I µi = 1014–1016 Pa sI scaling for Ganymede
I qs∼5–15 mW m−2
I Ganymede: H>400 kmI Titan: H∼50–300 km
→ Titan: melting at silicates interface and leaching of 40Ar?
-
Present-day bottom melting: Ganymede vs TitanI Titan, µi = 1015 Pa s: qcs ∝ HI µi = 1014–1016 Pa s
I scaling for Ganymede
I qs∼5–15 mW m−2
I Ganymede: H>400 kmI Titan: H∼50–300 km
→ Titan: melting at silicates interface and leaching of 40Ar?
-
Present-day bottom melting: Ganymede vs TitanI Titan, µi = 1015 Pa s: qcs ∝ HI µi = 1014–1016 Pa sI scaling for Ganymede
I qs∼5–15 mW m−2
I Ganymede: H>400 kmI Titan: H∼50–300 km
→ Titan: melting at silicates interface and leaching of 40Ar?
-
Present-day bottom melting: Ganymede vs TitanI Titan, µi = 1015 Pa s: qcs ∝ HI µi = 1014–1016 Pa sI scaling for Ganymede
I qs∼5–15 mW m−2
I Ganymede: H>400 kmI Titan: H∼50–300 km
→ Titan: melting at silicates interface and leaching of 40Ar?
-
Present-day bottom melting: Ganymede vs TitanI Titan, µi = 1015 Pa s: qcs ∝ HI µi = 1014–1016 Pa sI scaling for Ganymede
I qs∼5–15 mW m−2
I Ganymede: H>400 km
I Titan: H∼50–300 km
→ Titan: melting at silicates interface and leaching of 40Ar?
-
Present-day bottom melting: Ganymede vs TitanI Titan, µi = 1015 Pa s: qcs ∝ HI µi = 1014–1016 Pa sI scaling for Ganymede
I qs∼5–15 mW m−2
I Ganymede: H>400 kmI Titan: H∼50–300 km
→ Titan: melting at silicates interface and leaching of 40Ar?
-
Present-day bottom melting: Ganymede vs TitanI Titan, µi = 1015 Pa s: qcs ∝ HI µi = 1014–1016 Pa sI scaling for Ganymede
I qs∼5–15 mW m−2
I Ganymede: H>400 kmI Titan: H∼50–300 km
→ Titan: melting at silicates interface and leaching of 40Ar?
-
Conclusions
I two-phase model necessary to address melt evolution
I melting at the interface with silicates → volatiles leachingI small amount of water (φ∼few %)I volatiles transfered by upwelling plumes → extraction into ocean
I Ganymede: exchange more likely early in its evolutionI Titan: exchange possibly ongoing: transport of 40Ar into the ocean?
I further development: effect of salt & ammonia on Tm and ∆ρI thermo-chemical evolution model → Cassini, JUICE & Dragonfly
Thank you for yourattention!
-
Conclusions
I two-phase model necessary to address melt evolution
I melting at the interface with silicates → volatiles leachingI small amount of water (φ∼few %)I volatiles transfered by upwelling plumes → extraction into ocean
I Ganymede: exchange more likely early in its evolutionI Titan: exchange possibly ongoing: transport of 40Ar into the ocean?
I further development: effect of salt & ammonia on Tm and ∆ρI thermo-chemical evolution model → Cassini, JUICE & Dragonfly
Thank you for yourattention!
-
Conclusions
I two-phase model necessary to address melt evolution
I melting at the interface with silicates → volatiles leachingI small amount of water (φ∼few %)I volatiles transfered by upwelling plumes → extraction into ocean
I Ganymede: exchange more likely early in its evolution
I Titan: exchange possibly ongoing: transport of 40Ar into the ocean?
I further development: effect of salt & ammonia on Tm and ∆ρI thermo-chemical evolution model → Cassini, JUICE & Dragonfly
Thank you for yourattention!
-
Conclusions
I two-phase model necessary to address melt evolution
I melting at the interface with silicates → volatiles leachingI small amount of water (φ∼few %)I volatiles transfered by upwelling plumes → extraction into ocean
I Ganymede: exchange more likely early in its evolutionI Titan: exchange possibly ongoing: transport of 40Ar into the ocean?
I further development: effect of salt & ammonia on Tm and ∆ρI thermo-chemical evolution model → Cassini, JUICE & Dragonfly
Thank you for yourattention!
-
Conclusions & perspectives
I two-phase model necessary to address melt evolution
I melting at the interface with silicates → volatiles leachingI small amount of water (φ∼few %)I volatiles transfered by upwelling plumes → extraction into ocean
I Ganymede: exchange more likely early in its evolutionI Titan: exchange possibly ongoing: transport of 40Ar into the ocean?
I further development: effect of salt & ammonia on Tm and ∆ρ
I thermo-chemical evolution model → Cassini, JUICE & Dragonfly
Thank you for yourattention!
-
Conclusions & perspectives
I two-phase model necessary to address melt evolution
I melting at the interface with silicates → volatiles leachingI small amount of water (φ∼few %)I volatiles transfered by upwelling plumes → extraction into ocean
I Ganymede: exchange more likely early in its evolutionI Titan: exchange possibly ongoing: transport of 40Ar into the ocean?
I further development: effect of salt & ammonia on Tm and ∆ρI thermo-chemical evolution model → Cassini, JUICE & Dragonfly
Thank you for yourattention!
-
Conclusions & perspectives
I two-phase model necessary to address melt evolution
I melting at the interface with silicates → volatiles leachingI small amount of water (φ∼few %)I volatiles transfered by upwelling plumes → extraction into ocean
I Ganymede: exchange more likely early in its evolutionI Titan: exchange possibly ongoing: transport of 40Ar into the ocean?
I further development: effect of salt & ammonia on Tm and ∆ρI thermal evolution model → Cassini, JUICE & Dragonfly
Thank you for yourattention!
-
References
- Allègre + (2016), Geophys. Res. Lett., 23, 3555–3557.
- Alnaes + (2015), University of Cambridge.
- Bercovici + (1986), Geophys. Res. Lett., 13, 448–451.
- Bercovici + (2001), J. Geophys. Res., 106, 8887–8906.
- Bland + (2009), Icarus, 200, 207–221.
- Choblet + (2017), Icarus, 285, 252–262.
- Fortes + (2007), Icarus, 188, 139–153.
- Grasset & Sotin (1996), Icarus, 123, 101–112.
- Grindrod + (2008), Icarus, 197, 137–151.
- Jarvis (1984), Phys. Earth Planet. Inter., 36, 305–327.
- Journaux & Noack (2015), EPSC, EPSC2015-774.
- Kirk & Stevenson (1987), Icarus, 69, 91–134.
- Logg + (2012), Springer-Verlag, Berlin Heidelberg.
- Mitrovica & Jarvis (1987), Geophys. Astro. Fluid, 38, 193–224.
- Noack + (2016), Icarus, 277, 215–236.
- Showman & Malhotra (1997), Icarus, 127, 93–111.
- Sotin & Parmentier (1989), Phys. Earth Planet. Inter., 55, 10–25.
- Šrámek + (2007), Geophys. J. Int., 168, 964–982.
- Tobie + (2005), Icarus, 175, 496–502.
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