Jerome A. Neufeld
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Jerome A. Neufeld has a total of 110 co-authors. Here are the top co-authors by number of shared publications:
- Duncan Robin Hewitt
University of Cambridge
16 shared publications Herbert E. Huppert
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, CMS, Cambridge CB3 0WA, UK
11 shared publications- Katarzyna L. P. Warburton
Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge UK
9 shared publications John R. Lister
Department of Applied Mathematics and Theoretical Physics, Institute of Theoretical Geophysics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
8 shared publications- Kathryn Dodds
Earth Sciences, University of Cambridge, Downing Street, Cambridge, United Kingdom, CB2 3EQ
8 shared publications - Michael J. Bickle
Department of Earth Sciences University of Cambridge Cambridge UK
6 shared publications
Latest Publications
- Open Access
- 31 August 2026
- Published by Wiley
Inwards core crystallisation in asteroids: insights from laboratory experiments.
Given their small sizes, the cores of meteorite parent bodies likely crystallized inwardly from their core-mantle boundary (CMB). However, the iron snow model of dynamo generation that has been associated with Ganymede and Mars may not apply to these cores. This difference originates from the small adiabatic temperature difference between the CMB and interior of asteroids cores that may prevent remelting of the iron snow, removing the buoyancy source that could drive a dynamo field. Motivated by this, we have developed a set of analogue tank experiments to investigate the iron snow mode of core crystallization in asteroid cores. We find that the mean convective speeds of the fluid increase by approximately a factor of 2 when the fluid crystallizes. This increase in speed is driven by an increase in the bulk density of the fluid in the snow zone due to the presence of a small, entrained crystal fraction. We use our results to explore whether this mechanism can explain the records of dynamo activity recovered from paleomagnetic measurements of meteorites. We show that this mechanism can generate a similar magnitude of turbulence to the remelting-driven iron snow models, making it a possible dynamo mechanism for asteroid cores. Moreover, we consider the caveats of this mechanism, including the potential absence of a stably stratified snow zone and its dependence on crystal size. Finally, we highlight the experimental difficulty in inducing nucleation of solids away from a solid substrate, an observation which should be considered in future iron snow models.
- 31 August 2026
- Published by Wiley
Open AccessInwards core crystallisation in asteroids: insights from laboratory experiments.
Given their small sizes, the cores of meteorite parent bodies likely crystallized inwardly from their core-mantle boundary (CMB). However, the iron snow model of dynamo generation that has been associated with Ganymede and Mars may not apply to these cores. This difference originates from the small adiabatic temperature difference between the CMB and interior of asteroids cores that may prevent remelting of the iron snow, removing the buoyancy source that could drive a dynamo field. Motivated by this, we have developed a set of analogue tank experiments to investigate the iron snow mode of core crystallization in asteroid cores. We find that the mean convective speeds of the fluid increase by approximately a factor of 2 when the fluid crystallizes. This increase in speed is driven by an increase in the bulk density of the fluid in the snow zone due to the presence of a small, entrained crystal fraction. We use our results to explore whether this mechanism can explain the records of dynamo activity recovered from paleomagnetic measurements of meteorites. We show that this mechanism can generate a similar magnitude of turbulence to the remelting-driven iron snow models, making it a possible dynamo mechanism for asteroid cores. Moreover, we consider the caveats of this mechanism, including the potential absence of a stably stratified snow zone and its dependence on crystal size. Finally, we highlight the experimental difficulty in inducing nucleation of solids away from a solid substrate, an observation which should be considered in future iron snow models.
- Open Access
- 12 June 2026
- Published by California Digital Library (CDL) in EarthArXiv
Modelling the Evolution of Elliptical Röthlisberger Channels
Subglacial water flow is critical to basal sliding and ice dynamics. Modelling the coupled evolution of subglacial drainage and ice flow remains challenging, however. This study investigates the evolution of the basal ice-water interface by analysing heat and fluid flow in idealised englacial channels. We extend the classical Röthlisberger model for circular channels to elliptical channel geometries. A hybrid laminar–turbulent melt scheme captures heat generation and melting from both viscous and turbulent dissipation, while a viscous flow law models the creep closure of the surrounding ice. Whilst the flow of ice tends to increase the eccentricity of the channel, we find that elliptical channels tend toward a circular shape when laminar melting dominates due to differential melting between the roof and walls of the channel. Our hybrid melt model predicts the existence of stable, non-circular cross-sections. Unlike circular channels, these channels obey pressure-flux relationships that, beyond a critical volume flux threshold, suggest a preference for flux sharing, a behaviour characteristic of distributed drainage networks. This contrasts with circular channels, which undergo channelisation towards fewer, larger conduits. These idealised channels suggest potential simplifications to modelling subglacial drainage networks and the dynamics of evolving subglacial hydrological networks.
- 12 June 2026
- Published by California Digital Library (CDL) in EarthArXiv
Open AccessModelling the Evolution of Elliptical Röthlisberger Channels
Subglacial water flow is critical to basal sliding and ice dynamics. Modelling the coupled evolution of subglacial drainage and ice flow remains challenging, however. This study investigates the evolution of the basal ice-water interface by analysing heat and fluid flow in idealised englacial channels. We extend the classical Röthlisberger model for circular channels to elliptical channel geometries. A hybrid laminar–turbulent melt scheme captures heat generation and melting from both viscous and turbulent dissipation, while a viscous flow law models the creep closure of the surrounding ice. Whilst the flow of ice tends to increase the eccentricity of the channel, we find that elliptical channels tend toward a circular shape when laminar melting dominates due to differential melting between the roof and walls of the channel. Our hybrid melt model predicts the existence of stable, non-circular cross-sections. Unlike circular channels, these channels obey pressure-flux relationships that, beyond a critical volume flux threshold, suggest a preference for flux sharing, a behaviour characteristic of distributed drainage networks. This contrasts with circular channels, which undergo channelisation towards fewer, larger conduits. These idealised channels suggest potential simplifications to modelling subglacial drainage networks and the dynamics of evolving subglacial hydrological networks.
- Open Access
- 8 June 2026
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Planets
- Vol. 131 (6)
Lunar Crustal Formation by Melt Migration and Differentiation Within a Stagnant Lid
The lunar anorthosite highlands represent the Moon's primary crust, which formed during the solidification of a magma ocean following the Moon-forming giant impact. However, the canonical model of anorthite flotation in the crystallizing magma ocean often struggles to reproduce the long 200 Myr solidification timescale required by the ages of the anorthosite suite, as well as their diverse magmatic histories and the overlap in ages with the Mg-suite. If instead the anorthite crystals remain entrained in the magma ocean due to vigorous convection, the magma ocean behaves as a liquid-crystal slurry with a rigid immobile lid at the surface which reduces the cooling rate of the magma ocean and results in long solidification times. Here, we investigate whether sufficient differentiation can occur within the stagnant lid due to upward melt migration and compaction of the solid to produce an anorthite-rich crust. Our model consists of a simplified two-component anorthite-olivine melt system, which becomes progressively enriched in anorthite due to a forced inflow of anorthite-rich melt at a constant rate to the lid base. We find that large-scale anorthite enrichment and shallow emplacement of anorthite-rich melt can take place if the partially molten zone is thick enough to allow the formation of porosity waves, and if the rate of latent heat production is greater than the rate of lid cooling. We also demonstrate that crystal flotation is likely to be able to occur in these anorthite-rich melt regions, resulting in fractional crystallization which could produce anorthosite massifs.- 8 June 2026
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Planets
- Vol. 131 (6)
Open AccessLunar Crustal Formation by Melt Migration and Differentiation Within a Stagnant Lid
The lunar anorthosite highlands represent the Moon's primary crust, which formed during the solidification of a magma ocean following the Moon-forming giant impact. However, the canonical model of anorthite flotation in the crystallizing magma ocean often struggles to reproduce the long 200 Myr solidification timescale required by the ages of the anorthosite suite, as well as their diverse magmatic histories and the overlap in ages with the Mg-suite. If instead the anorthite crystals remain entrained in the magma ocean due to vigorous convection, the magma ocean behaves as a liquid-crystal slurry with a rigid immobile lid at the surface which reduces the cooling rate of the magma ocean and results in long solidification times. Here, we investigate whether sufficient differentiation can occur within the stagnant lid due to upward melt migration and compaction of the solid to produce an anorthite-rich crust. Our model consists of a simplified two-component anorthite-olivine melt system, which becomes progressively enriched in anorthite due to a forced inflow of anorthite-rich melt at a constant rate to the lid base. We find that large-scale anorthite enrichment and shallow emplacement of anorthite-rich melt can take place if the partially molten zone is thick enough to allow the formation of porosity waves, and if the rate of latent heat production is greater than the rate of lid cooling. We also demonstrate that crystal flotation is likely to be able to occur in these anorthite-rich melt regions, resulting in fractional crystallization which could produce anorthosite massifs. - Open Access
- 14 March 2026
- Published by Copernicus GmbH
Elliptical Röthlisberger Channels: Modelling Flow, Heat and Evolution
Subglacial water flow plays a critical role in basal sliding and, consequently, in glacier and ice-sheet dynamics. However, modelling the coupled evolution of subglacial drainage and ice flow remains challenging. This study investigates the evolution of the basal ice–water interface by analysing heat and fluid flow in idealised englacial channels. We extend the classical Röthlisberger model for circular channels to elliptical channel geometries. A hybrid turbulent–laminar melt scheme captures heat generation from both viscous and turbulent dissipation, while a viscous flow law models the creep closure of the surrounding ice. The flow and temperature profiles in elliptical channels are solved for with differential melting between the roof and walls of the channel. We find that elliptical channels tend towards a circular shape when laminar melting dominates, whilst the flow of ice tends to increase the eccentricity of the channel. Our hybrid laminar-turbulent melt model permits variations in the distribution of melting along the ice-water boundary and the existence of stable, non-circular cross-sections. These stable channels obey pressure-flux relationships that we use to explore the evolution and dynamics of hydrologically interacting channels in a wider subglacial drainage network, working towards a simplified and scalable subglacial hydrology model.
- 14 March 2026
- Published by Copernicus GmbH
Open AccessElliptical Röthlisberger Channels: Modelling Flow, Heat and Evolution
Subglacial water flow plays a critical role in basal sliding and, consequently, in glacier and ice-sheet dynamics. However, modelling the coupled evolution of subglacial drainage and ice flow remains challenging. This study investigates the evolution of the basal ice–water interface by analysing heat and fluid flow in idealised englacial channels. We extend the classical Röthlisberger model for circular channels to elliptical channel geometries. A hybrid turbulent–laminar melt scheme captures heat generation from both viscous and turbulent dissipation, while a viscous flow law models the creep closure of the surrounding ice. The flow and temperature profiles in elliptical channels are solved for with differential melting between the roof and walls of the channel. We find that elliptical channels tend towards a circular shape when laminar melting dominates, whilst the flow of ice tends to increase the eccentricity of the channel. Our hybrid laminar-turbulent melt model permits variations in the distribution of melting along the ice-water boundary and the existence of stable, non-circular cross-sections. These stable channels obey pressure-flux relationships that we use to explore the evolution and dynamics of hydrologically interacting channels in a wider subglacial drainage network, working towards a simplified and scalable subglacial hydrology model.
- Open Access
- 14 March 2026
- Published by Copernicus GmbH
Quantifying melt rates in Antarctic grounding zones using flexural inversion
Antarctic ice shelves in the Amundsen Sea embayment are vulnerable to rapid disintegration, the dynamics of which depend strongly on the rate of melting of the ice shelf. In particular, melt rates in the grounding zone - where ice transiently makes contact with the bedrock - have proven difficult to measure using remote methods which rely on remote measurements of the ice freeboard and an application of the hydrostatic approximation. Here, we extend existing remote observations of melt rates into the grounding zone by incorporating a model of the elastic flexure of ice shelves. The numerical model is tested against existing analytical models, and then demonstrated on select ice shelves in the Amunsdsen sea embayment. Melt rates are found which are comparable with existing hydrostatic estimates away from the grounding zone, but are more continuous within the region of transient contact with the bedrock.
- 14 March 2026
- Published by Copernicus GmbH
Open AccessQuantifying melt rates in Antarctic grounding zones using flexural inversion
Antarctic ice shelves in the Amundsen Sea embayment are vulnerable to rapid disintegration, the dynamics of which depend strongly on the rate of melting of the ice shelf. In particular, melt rates in the grounding zone - where ice transiently makes contact with the bedrock - have proven difficult to measure using remote methods which rely on remote measurements of the ice freeboard and an application of the hydrostatic approximation. Here, we extend existing remote observations of melt rates into the grounding zone by incorporating a model of the elastic flexure of ice shelves. The numerical model is tested against existing analytical models, and then demonstrated on select ice shelves in the Amunsdsen sea embayment. Melt rates are found which are comparable with existing hydrostatic estimates away from the grounding zone, but are more continuous within the region of transient contact with the bedrock.
- Open Access
- 24 February 2026
- Published by California Digital Library (CDL) in EarthArXiv
Rethinking grounding-zone basal drag for improved projections of Antarctic ice loss
Ice-stream grounding zones are critical parts of the Antarctic Ice Sheet and we must be able to model how they retreat with confidence. This is because for most of Antarctica, the grounding-zone location determines the flux of ice to the ocean. As such, future grounding-zone locations (as the ice-sheet edge retreats inland) dictate the pattern and rate of ice loss and the associated sea-level rise. Ice flow across the grounding zone is opposed by a combination of ice-shelf buttressing if lateral drag or pinning points are present, and by friction between the ice and its bed - basal drag. While the loss of buttressing and ocean-forced melting of ice shelves are popular research foci, far less attention is paid to resistance at the bed. Here, we revisit the treatment of grounding zones in models and argue for a new approach to basal drag: evolving bed conditions result in highly variable drag that is not captured by existing sliding laws. We begin by reviewing the complex basal processes operating in grounding zones over different timescales, such as tides, evolving subglacial hydrology, and sedimentation. Then, to illustrate the significance of the basal drag term, we run retreat scenarios in the UFEMISM model using an accepted basal sliding law that only varies in its treatment of subglacial hydrology (via effective pressure). Appreciable differences in retreat patterns motivate us to consider how modelling grounding zones may be improved. To reduce uncertainty in ice-loss projections, in tandem with refining ice-shelf melt parameterisations, careful observations from grounding zones and physically-based basal drag parameterisations are required.
- 24 February 2026
- Published by California Digital Library (CDL) in EarthArXiv
Open AccessRethinking grounding-zone basal drag for improved projections of Antarctic ice loss
Ice-stream grounding zones are critical parts of the Antarctic Ice Sheet and we must be able to model how they retreat with confidence. This is because for most of Antarctica, the grounding-zone location determines the flux of ice to the ocean. As such, future grounding-zone locations (as the ice-sheet edge retreats inland) dictate the pattern and rate of ice loss and the associated sea-level rise. Ice flow across the grounding zone is opposed by a combination of ice-shelf buttressing if lateral drag or pinning points are present, and by friction between the ice and its bed - basal drag. While the loss of buttressing and ocean-forced melting of ice shelves are popular research foci, far less attention is paid to resistance at the bed. Here, we revisit the treatment of grounding zones in models and argue for a new approach to basal drag: evolving bed conditions result in highly variable drag that is not captured by existing sliding laws. We begin by reviewing the complex basal processes operating in grounding zones over different timescales, such as tides, evolving subglacial hydrology, and sedimentation. Then, to illustrate the significance of the basal drag term, we run retreat scenarios in the UFEMISM model using an accepted basal sliding law that only varies in its treatment of subglacial hydrology (via effective pressure). Appreciable differences in retreat patterns motivate us to consider how modelling grounding zones may be improved. To reduce uncertainty in ice-loss projections, in tandem with refining ice-shelf melt parameterisations, careful observations from grounding zones and physically-based basal drag parameterisations are required.
- Open Access
- 2 December 2025
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 1024
Response of a gravity current in a porous medium to a perturbation of the permeability field
One of the challenges with modelling subsurface flows is the uncertainty in measurements of geological properties, mostly due to limited resolution in observation methods. Many subsurface flows can be modelled as a gravity current, which, for uniform material properties and power-law injection rate, has a well-characterised similarity solution. The similarity solution forms a dynamical attractor that is typically approached rapidly from a host of initial conditions. Here, we consider the impact of transverse variations to the permeability field by performing a perturbation analysis of the self-similar spreading. This treats the response as perturbations to the self-similar flow. We restrict our focus to permeability fields that vary laterally, or across the flow, starting with the simple case of a sinusoidal perturbation to a uniform permeability. At early times, the height and nose position of the current are determined by the local permeability, and deviations to the height and nose grow at the same rate as the mean, and proportional to the amplitude, of the permeability variation. The transition between the early and late time regimes is governed by the wavelength of the permeability. At late times, lateral spreading between high and low permeability streaks is dominant; the height deviations decay, and the nose deviations approach a steady state. The magnitudes of both depend on the product of the wavelength and amplitude of the permeability. The single mode sets the groundwork for examining more complex, multimodal permeabilities, which are more representative of real geological structures.
- 2 December 2025
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 1024
Open AccessResponse of a gravity current in a porous medium to a perturbation of the permeability field
One of the challenges with modelling subsurface flows is the uncertainty in measurements of geological properties, mostly due to limited resolution in observation methods. Many subsurface flows can be modelled as a gravity current, which, for uniform material properties and power-law injection rate, has a well-characterised similarity solution. The similarity solution forms a dynamical attractor that is typically approached rapidly from a host of initial conditions. Here, we consider the impact of transverse variations to the permeability field by performing a perturbation analysis of the self-similar spreading. This treats the response as perturbations to the self-similar flow. We restrict our focus to permeability fields that vary laterally, or across the flow, starting with the simple case of a sinusoidal perturbation to a uniform permeability. At early times, the height and nose position of the current are determined by the local permeability, and deviations to the height and nose grow at the same rate as the mean, and proportional to the amplitude, of the permeability variation. The transition between the early and late time regimes is governed by the wavelength of the permeability. At late times, lateral spreading between high and low permeability streaks is dominant; the height deviations decay, and the nose deviations approach a steady state. The magnitudes of both depend on the product of the wavelength and amplitude of the permeability. The single mode sets the groundwork for examining more complex, multimodal permeabilities, which are more representative of real geological structures.
- Open Access
- 27 September 2025
- Published by Elsevier in Journal of Non-Newtonian Fluid Mechanics
- Vol. 346
Wrinkling of a viscoplastic plate on a viscous substrate
- 27 September 2025
- Published by Elsevier in Journal of Non-Newtonian Fluid Mechanics
- Vol. 346
Open AccessWrinkling of a viscoplastic plate on a viscous substrate
- Open Access
- 14 August 2025
- Published by Wiley
Lunar crustal formation by melt migration and differentiation within a stagnant lid.
The lunar anorthosite highlands represent the Moon’s primary crust, which formed during the solidification of a magma ocean following the Moon-forming giant impact. However, the canonical model of anorthite flotation in the crystallising magma ocean often struggles to reproduce the long > 200 Myr solidification timescale required by the ages of the anorthosite suite, as well as their diverse magmatic histories and the overlap in ages with the Mg-suite. If instead the anorthite crystals remain entrained in magma ocean due to vigorous convection, the magma ocean behaves as a liquid-crystal slurry with a rigid immobile lid at the surface, which reduces the cooling rate of the magma ocean and results in long solidification times. Here, we investigate whether sufficient melt differentiation and migration can occur via viscous compaction of the solid within the stagnant lid to produce an anorthite-rich crust. Our model consists of a simplified two-component anorthite-olivine melt system, which becomes progressively enriched in anorthite as the melt solidifies. We calculate the thermochemical evolution of this melt as it rises through a stagnant lid, cools and solidifies. We find that large-scale anorthite enrichment and shallow emplacement of anorthite-rich melt can take place if the partially molten zone is thick enough to allow the formation of porosity waves, and if the rate of melt advection is greater than the rate of lid cooling. We also demonstrate that crystal flotation is likely to be able to occur in these anorthite-rich melt regions, resulting in fractional crystallisation which could produce anorthosite massifs.
- 14 August 2025
- Published by Wiley
Open AccessLunar crustal formation by melt migration and differentiation within a stagnant lid.
The lunar anorthosite highlands represent the Moon’s primary crust, which formed during the solidification of a magma ocean following the Moon-forming giant impact. However, the canonical model of anorthite flotation in the crystallising magma ocean often struggles to reproduce the long > 200 Myr solidification timescale required by the ages of the anorthosite suite, as well as their diverse magmatic histories and the overlap in ages with the Mg-suite. If instead the anorthite crystals remain entrained in magma ocean due to vigorous convection, the magma ocean behaves as a liquid-crystal slurry with a rigid immobile lid at the surface, which reduces the cooling rate of the magma ocean and results in long solidification times. Here, we investigate whether sufficient melt differentiation and migration can occur via viscous compaction of the solid within the stagnant lid to produce an anorthite-rich crust. Our model consists of a simplified two-component anorthite-olivine melt system, which becomes progressively enriched in anorthite as the melt solidifies. We calculate the thermochemical evolution of this melt as it rises through a stagnant lid, cools and solidifies. We find that large-scale anorthite enrichment and shallow emplacement of anorthite-rich melt can take place if the partially molten zone is thick enough to allow the formation of porosity waves, and if the rate of melt advection is greater than the rate of lid cooling. We also demonstrate that crystal flotation is likely to be able to occur in these anorthite-rich melt regions, resulting in fractional crystallisation which could produce anorthosite massifs.
- Open Access
- 20 January 2025
- Published by Copernicus GmbH
Joule-Thomson cooling and phase transitions during CO2 injection in depleted reservoirs
Depleted oil and gas reservoirs are attractive sites for CO2 sequestration. However, the injection of CO2 into depleted reservoirs carries the potential for significant Joule-Thomson cooling, when dense, supercritical CO2 is injected into a low-pressure reservoir. The resulting low temperatures around the well-bore risk causing thermal fracturing and/or freezing of pore waters or precipitation of gas hydrates which would reduce injectivity and jeopardise near-well stability. Injection into reservoirs at subcritical pressure also leads to a phase transition from liquid to vapour CO2. This is accompanied by cooling, due to the latent heat of vaporisation, and dramatic changes in fluid properties including density, compressibility and viscosity.We present models of non-isothermal flow of CO2 in the near well-bore region, which demonstrate the controls on cooling and constrain the different pressure-temperature regimes that can emerge. We show that during radial injection, with fixed injection rate, transient Joule-Thomson cooling can be described by similarity solutions at early times. The positions of the CO2 and thermal fronts are described by self-similar scaling relations. The scaling analysis here identifies the parametric dependence of Joule-Thomson cooling. We present a sensitivity analysis which demonstrates that the primary controls on the degree of cooling are the injection rate and Joule-Thomson coefficient. The analysis presented provides a computationally efficient approach to assessing the degree of Joule-Thomson cooling expected during injection start-up, providing a complement to full numerical simulations.
- 20 January 2025
- Published by Copernicus GmbH
Open AccessJoule-Thomson cooling and phase transitions during CO2 injection in depleted reservoirs
Depleted oil and gas reservoirs are attractive sites for CO2 sequestration. However, the injection of CO2 into depleted reservoirs carries the potential for significant Joule-Thomson cooling, when dense, supercritical CO2 is injected into a low-pressure reservoir. The resulting low temperatures around the well-bore risk causing thermal fracturing and/or freezing of pore waters or precipitation of gas hydrates which would reduce injectivity and jeopardise near-well stability. Injection into reservoirs at subcritical pressure also leads to a phase transition from liquid to vapour CO2. This is accompanied by cooling, due to the latent heat of vaporisation, and dramatic changes in fluid properties including density, compressibility and viscosity.We present models of non-isothermal flow of CO2 in the near well-bore region, which demonstrate the controls on cooling and constrain the different pressure-temperature regimes that can emerge. We show that during radial injection, with fixed injection rate, transient Joule-Thomson cooling can be described by similarity solutions at early times. The positions of the CO2 and thermal fronts are described by self-similar scaling relations. The scaling analysis here identifies the parametric dependence of Joule-Thomson cooling. We present a sensitivity analysis which demonstrates that the primary controls on the degree of cooling are the injection rate and Joule-Thomson coefficient. The analysis presented provides a computationally efficient approach to assessing the degree of Joule-Thomson cooling expected during injection start-up, providing a complement to full numerical simulations.