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Funding: This research received funding from the European Research Council under Horizon 2020 research and innovation program grant agreement number 772255. The authors thank the Isaac Newton Institute for Mathematical Sciences for its hospitality during the programme Melt in the Mantle which was supported by EPSRC Grant Number EP/K032208/1. Melt extraction from the partially molten mantle is among the fundamental processes shaping the solid Earth today and over geological time. A diversity of properties and mechanisms contribute to the physics of melt extraction. We review progress of the past ∼25 years of research in this area, with a focus on understanding the speed and style of buoyancy-driven melt extraction. Observations of U-series disequilibria in young lavas and the surge of deglacial volcanism in Iceland suggest this speed is rapid compared to that predicted by the null hypothesis of diffuse porous flow. The discrepancy indicates that the style of extraction is channelized. We discuss how channelization is sensitive to mechanical and thermochemical properties and feedbacks, and to asthenospheric heterogeneity. We review the grain-scale physics that underpins these properties and hence determines the physical behavior at much larger scales. We then discuss how the speed of melt extraction is crucial to predicting the magmatic response to glacial and sea-level variations. Finally, we assess the frontier of current research and identify areas where significant advances are expected over the next 25 years. In particular, we highlight the coupling of melt extraction with more realistic models of mantle thermochemistry and rheological properties. This coupling will be crucial in understanding complex settings such as subduction zones. ▪ Mantle melt extraction shapes Earth today and over geological time. ▪ Observations, lab experiments, and theory indicate that melt ascends through the mantle at speeds ∼30 m/year by reactively channelized porous flow. ▪ Variations in sea level and glacial ice loading can cause significant changes in melt supply to submarine and subaerial volcanoes. ▪ Fluid-driven fracture is important in the lithosphere and, perhaps, in the mantle wedge of subduction zones, but remains a challenge to model. Preprint

The amount of H$_2$O and CO$_2$ that is carried into deep mantle by subduction beyond subarc depths is of fundamental importance to the deep volatile cycle but remains debated. Given the large uncertainties surrounding the spatio-temporal pattern of fluid flow and the equilibrium state within subducting slabs, a model of H$_2$O and CO$_2$ transport in slabs should be balanced between model simplicity and capability. We construct such a model in a two-part contribution. In this Part I of our contribution, thermodynamic parameterization is performed for the devolatilization of representative subducting materials---sediments, basalts, gabbros, peridotites. The parameterization avoids reproducing the details of specific devolatilization reactions, but instead captures the overall behaviors of coupled (de)hydration and (de)carbonation. Two general, leading-order features of devolatilization are captured: (1) the released volatiles are H$_2$O-rich near the onset of devolatilization; (2) increase of the ratio of bulk CO$_2$ over H$_2$O inhibits overall devolatilization and thus lessens decarbonation. These two features play an important role in simulation of volatile fractionation and infiltration in thermodynamically open systems. When constructing the reactive fluid flow model of slab H$_2$O and CO$_2$ transport in the companion paper Part II, this parameterization can be incorporated to efficiently account for the open-system effects of H$_2$O and CO$_2$ transport., Comment: accepted version in Geochemistry, Geophysics, Geosystems, but re-typeset

We present a study on the dynamic fracture and fragmentation of Ti-6Al-4V cylinders at initial temperatures ranging from approximately 150 K to 750 K. Cylinders with an inner diameter of 50 mm and a wall thickness of 4 mm were driven into uniform axially-symmetric expansion at radial strain rates of 104 s−1 using the ogive-insert gas gun method. Diagnostics consisted of simultaneous high speed imaging and multiple points of laser velocimetry (PDV) along the length of the sample. The imaging and PDV provided a record of the expansion process, giving expansion velocity and the failure strain. Recovered fragments were examined with optical and scanning electron microscopy and electron backscatter diffraction techniques to determine the fracture mechanisms for each initial temperature. The failure strain (radial strain at first fracture) was observed to increase with temperature over the range tested, from 7.4 ± 5.2 percent at 158 K to 24.1 ± 2.4 percent at 724 K. In experiments from 158 K up to 609 K the fracture mechanism was found to be ductile tearing under mode II loading along the planes of maximum shear at 45° to the radius. At an initial cylinder temperature of 724 K the fracture mechanism transitioned to void nucleation and coalescence along adiabatic shear bands, again forming at 45° to the radial direction. The fragmentation toughness Kf was observed to also increase with temperature until the 724 K shot where there was a marked reduction, suggesting the formation of shear bands at high temperatures reduced the energy required to form fragments. The average value of Kf was 101 ± 13 MPa m1/2.

Subduction is a crucial part of the long-term water and carbon cycling between Earth's exosphere and interior. However, there is broad disagreement over how much water and carbon is liberated from subducting slabs to the mantle wedge and transported to island-arc volcanoes. In the companion paper Part I, we parameterize the metamorphic reactions involving H$_2$O and CO$_2$ for representative subducting lithologies. On this basis, a two-dimensional reactive transport model is constructed in this Part II. We assess the various controlling factors of CO$_2$ and H$_2$O release from subducting slabs. Model results show that up-slab fluid flow directions produce a flux peak of CO$_2$ and H$_2$O at subarc depths. Moreover, infiltration of H$_2$O-rich fluids sourced from hydrated slab mantle enhances decarbonation or carbonation at lithological interfaces, increases slab surface fluxes, and redistributes CO$_2$ from basalt and gabbro layers to the overlying sedimentary layer. As a result, removal of the cap sediments (by diapirism or off-scraping) leads to elevated slab surface CO$_2$ and H$_2$O fluxes. The modelled subduction efficiency (the percentage of initially subducted volatiles retained until $\sim$200 km deep) of H$_2$O and CO$_2$ is increased by open-system effects due to fractionation within the interior of lithological layers., accepted version in Geochemistry, Geophysics, Geosystems, but re-typeset

Partial melting of asthenospheric mantle generates magma that supplies volcanic systems. The timescale of melt extraction from the mantle has been hotly debated. Microstructural measurements of permeability typically suggest relatively slow melt extraction (1 m/yr) whereas geochemical (Uranium-decay series) and geophysical observations suggest much faster melt extraction (100 m/yr). The deglaciation of Iceland triggered additional mantle melting and magma flux at the surface. The rapid response has been used to argue for relatively rapid melt extraction. However, this episode must, at least to some extent, be unrepresentative, because the rates of magma eruption at the surface increased about thirty-fold relative to the steady state. Our goal is to quantify this unrepresentativeness. We develop a one-dimensional, time-dependent and nonlinear (far from steady-state), model forced by the most recent, and best mapped, Icelandic deglaciation. We find that 30 m/yr is the best estimate of the steady-state maximum melt velocity. This is a factor of about 3 smaller than previously claimed, but still relatively fast. We translate these estimates to other mid-ocean ridges accounting for differences in passive and active upwelling and degree of melting. We find that fast melt extraction greater than about 10 m/yr prevails globally., Accepted for publication in Earth and Planetary Science Letters (2020). Total 17 pages and 5 figures (including Supplementary Material)

The thermal evolution of melt ponds on Arctic sea ice was investigated through a combination of autonomous observations and two-dimensional high-resolution fluid dynamics simulations. We observed one relatively fresh pond and one saline pond on the same ice floe, with similar depth. The comparison of observations and simulations indicates that thermal convection dominates in relatively fresh ponds, but conductive heat transfer dominates in salt-stratified ponds. Using a parameterized surface energy balance, we estimate that the heat flux to the ice is larger under the saline pond than the freshwater pond when averaged over the observational period. The deviation is sensitive to assumed wind, varying between 3 and 14 W/m(2) for winds from 0 to 5 m/s. If this effect persists as conditions evolve through the melt season, our results suggest that this imbalance potentially has a climatologically significant impact on sea-ice evolution. Plain Language Summary Sea ice provides key feedbacks on polar and global climate, with melt ponds being particularly significant. Melt ponds darken the ice surface, thereby increasing the absorption of sunlight and accelerating ice melt. This study provides a new perspective on melt-pond salinity, its previously unrecognized significance in controlling the thermal properties of ponds, and the potential impact on ice melting as we transition toward a younger sea ice cover. Many state-of-the-art sea ice models represent melt ponds as a freshwater layer with a surface temperature of 0 degrees C, consistent with a past Arctic ocean dominated by desalinated perennial ice and relatively fresh ponds. However, perennial ice has diminished in recent decades, with increasing prevalence of young saline ice. This leads to ponds with a wider range of salinities and temperatures. We show that salinity strongly impacts pond temperatures, using observations of adjacent freshwater and saline melt ponds on Arctic sea ice. Combining this data with model simulations, we find that melt-pond salinity impacts heat transfer to the ice below and the resulting melting rate. Our study reveals that melt-pond salinity and salt stratification are key variables influencing heat transfer in melt ponds, which need to be considered in future model development.

Certain geological features have been interpreted as evidence of channelized magma flow in the mantle, which is a compacting porous medium. Aharonov et al. (1995) developed a simple model of reactive porous flow and numerically analysed its instability to channels. The instability relies on magma advection against a chemical solubility gradient and the porosity-dependent permeability of the porous host rock. We extend the previous analysis by systematically mapping out the parameter space. Crucially, we augment numerical solutions with asymptotic analysis to better understand the physical controls on the instability. We derive scalings for critical conditions of the instability and analyse the associated bifurcation structure. We also determine scalings for the wavelength and growth rate of the channel structures that emerge. We obtain quantitative theories for and a physical understanding of: first, how advection or diffusion over the reactive time scale set the horizontal length scale of channels; second, the role of viscous compaction of the host rock, which also affects the vertical extent of channelized flow. These scalings allow us to derive estimates of the dimensions of emergent channels that are consistent with the geologic record., Comment: 30 pages, 10 figures. Revised manuscript accepted for publication in the Journal of Fluid Mechanics

Magmatism in subduction zones builds continental crust and causes most of Earth's subaerial volcanism. The production rate and composition of magmas are controlled by the thermal structure of subduction zones. A range of geochemical and heat flow evidence has recently converged to indicate that subduction zones are hotter at lithospheric depths beneath the arc than predicted by canonical thermomechanical models, which neglect magmatism. We show that this discrepancy can be resolved by consideration of the heat transported by magma. In our one- and two-dimensional numerical models and scaling analysis, magmatic transport of sensible and latent heat locally alters the thermal structure of canonical models by $\sim$300 K, increasing predicted surface heat flow and mid-lithospheric temperatures to observed values. We find the advection of sensible heat to be larger than the deposition of latent heat. Based on these results we conclude that thermal transport by magma migration affects the chemistry and the location of arc volcanoes., Revised version. 10 pages, 9 figures (plus Supplementary Material: 5 pages, 4 figures). Changes: slightly expanded description of model and discussion of results

Recent thinning and ponding of Arctic sea ice may have led to frequent, extensive phytoplankton blooms under sea ice., In July 2011, the observation of a massive phytoplankton bloom underneath a sea ice–covered region of the Chukchi Sea shifted the scientific consensus that regions of the Arctic Ocean covered by sea ice were inhospitable to photosynthetic life. Although the impact of widespread phytoplankton blooms under sea ice on Arctic Ocean ecology and carbon fixation is potentially marked, the prevalence of these events in the modern Arctic and in the recent past is, to date, unknown. We investigate the timing, frequency, and evolution of these events over the past 30 years. Although sea ice strongly attenuates solar radiation, it has thinned significantly over the past 30 years. The thinner summertime Arctic sea ice is increasingly covered in melt ponds, which permit more light penetration than bare or snow-covered ice. Our model results indicate that the recent thinning of Arctic sea ice is the main cause of a marked increase in the prevalence of light conditions conducive to sub-ice blooms. We find that as little as 20 years ago, the conditions required for sub-ice blooms may have been uncommon, but their frequency has increased to the point that nearly 30% of the ice-covered Arctic Ocean in July permits sub-ice blooms. Recent climate change may have markedly altered the ecology of the Arctic Ocean.

We incorporate a physically derived parameterization of gravity drainage, in terms of a convective upwelling velocity, into a one-dimensional, thermodynamic sea- ice model of the kind currently used in coupled climate models. Our parameterization uses a local Rayleigh number to represent the important feedback between ice salinity, porosity, permeability and desalination rate. It allows us to determine salt fluxes from sea ice and the corresponding evolution of the bulk salinity of the ice, in contrast to older, established models that prescribe the ice salinity. This improves the predictive power of climate models in terms of buoyancy fluxes to the polar oceans, and also the thermal properties of sea ice, which depend on its salinity. We analyze the behaviour of exist- ing fixed-salinity models, elucidate the physics by which changing salinity affects ice growth and compare against our dynamic-salinity model, both in terms of laboratory experiments and also deep-ocean calculations. These comparisons explain why the direct effect of ice salinity on growth is relatively small (though not always negligible, and sometimes dif- ferent from previous studies), and also highlight substantial differences in the qualita- tive pattern and quantitative magnitude of salt fluxes into the polar oceans. Our study is particularly relevant to growing first-year ice, when gravity drainage is the dominant mechanism by which ice desalinates. We expect that our dynamic model, which respects the underlying physics of brine drainage, should be more robust to changes in polar cli- mate and more responsive to rapid changes in oceanic and atmospheric forcing.

Magmatism and volcanism transfer carbon from the solid Earth into the climate system. This transfer may be modulated by the glacial/interglacial cycling of water between oceans and continental ice sheets, which alters the surface loading of the solid Earth. The consequent volcanic-carbon fluctuations have been proposed as a pacing mechanism for Pleistocene glacial cycles. This mechanism is dependant on the amplitude and lag of the mid-ocean ridge response to sea-level changes. Here we develop and analyse a new model for that response, eliminating some questionable assumptions made in previous work. Our model calculates the carbon flux, accounting for the thermodynamic effect of mantle carbon: reduction of the solidus temperature and a deeper onset of melting. We analyse models forced by idealised, periodic sea level and conclude that fluctuations in melting rate are the prime control on magma and carbon flux. We also discuss a model forced by a reconstruction of eustatic sea level over the past 800 kyr. It indicates that peak-to-trough variations of magma and carbon flux are up to about 20% and 10% of the mean flux, respectively. Peaks in mid-ocean ridge emissions lag peaks in sea-level forcing by less than about 20 kyr and the lag could well be shorter. The amplitude and lag are sensitive to the rate of melt segregation. The lag is much shorter than the time it takes for melt to travel vertically across the melting region., 28 pages including supplementary material. 9 figures plus 6 supplementary figures. Accepted for publication in Earth and Planetary Science Letters

[1] Gravity drainage of brine through liquid brine channels is the dominant mechanism for the desalination of growing sea ice. We describe and determine mathematically the essential physics of this process, elucidating the connection between downward flow in brine channels and a convective upward flow in the rest of the porous ice, which we show has a vertically linear structure and strength proportional to a Rayleigh number. Our simple dynamical model of this process is used to interpret the exponential propagation of dye fronts in laboratory experiments. We propose that using our new, derived parameterization for gravity drainage in sea ice in terms of two unknown parameters could lead to computationally feasible improvements to thermodynamic sea-ice models.

The physics of ice crystal growth from the liquid phase, especially in the presence of salt, has received much less attention than the growth of snow crystals from the vapour phase. The growth of so-called frazil ice by solidification of a supercooled aqueous salt solution is consistent with crystal growth in the basal plane being limited by the diffusive removal of the latent heat of solidification from the solid--liquid interface, while being limited by attachment kinetics in the perpendicular direction. This leads to the formation of approximately disk-shaped crystals with a low aspect ratio of thickness compared to radius, because radial growth is much faster than axial growth. We calculate numerically how fast disk-shaped crystals grow in both pure and binary melts, accounting for the comparatively slow axial growth, the effect of dissolved solute in the fluid phase and the difference in thermal properties between solid and fluid phases. We identify the main physical mechanisms that control crystal growth and show that the diffusive removal of both the latent heat released and also the salt rejected at the growing interface are significant. Our calculations demonstrate that certain previous parameterizations, based on scaling arguments, substantially underestimate crystal growth rates by a factor of order 10-100 for low aspect ratio disks, and provide a parameterization for use in models of ice crystal growth in environmental settings., 11 pages, 9 figures. Updated version with some additional discussion and references, mostly in the introduction. We tested a further two models of axial growth in section III, and added a new figure in that section

The free-boundary problem between a liquid region and a mushy layer (a reactive porous medium) must respect both thermodynamic and fluid dynamical considerations. We develop a steady two-dimensional forced-flow configuration to investigate the thermodynamic condition of marginal equilibrium that applies to a solidifying mushy layer with outflow and requires that streamlines are tangent to isotherms at the interface. We show that a ‘two-domain’ approach in which the mushy layer and liquid region are distinct domains is consistent with marginal equilibrium by extending the Stokes equations in a narrow transition region within the mushy layer. We show that the tangential fluid velocity changes rapidly in the transition region to satisfy marginal equilibrium. In convecting mushy layers with liquid channels, a buoyancy gradient can drive this tangential flow. We use asymptotic analysis in the limit of small Darcy number to derive a regime diagram for the existence of steady solutions. Thus we show that marginal equilibrium is a robust boundary condition and can be used without precise knowledge of the fluid flow near the interface.

Solute transport within solidifying binary alloys occurs predominantly by convection from narrow liquid chimneys within a porous mushy layer. We develop a simple model that elucidates the dominant structure and driving forces of the flow, which could be applied to modelling brine fluxes from sea ice, where a cheaply implementable approach is essential. A horizontal density gradient within the mushy layer in the vicinity of the chimneys leads to baroclinic torque which sustains the convective flow. In the bulk of the mushy layer, the isotherms are essentially horizontal. In this region, we impose a vertically linear temperature field and immediately find that the flow field is a simple corner flow. We determine the strength of this flow by finding a similarity solution to the governing mushy-layer equations in an active region near the chimney. We also determine the corresponding shape of the chimney, the vertical structure of the solid fraction and the interstitial flow field. We apply this model first to a periodic, planar array of chimneys and show analytically that the solute flux through the chimneys is proportional to a mush Rayleigh number. Secondly we extend the model to three dimensions and find that an array of chimneys can be characterized by the average drainage area alone. Therefore we solve the model in an axisymmetric geometry and find new, sometimes nonlinear, relationships between the solute flux, the Rayleigh number and the other dimensionless parameters of the system.

Significant changes in the state of the Arctic ice cover are occurring. As the summertime extent of sea ice diminishes, the Arctic is increasingly characterized by first-year rather than multi-year ice. It is during the early stages of ice growth that most brine is injected into the oceans, contributing to the buoyancy flux that mediates the thermo-haline circulation. Current operational sea-ice components of climate models often treat brine rejection between sea ice and the ocean similarly to a thermodynamic segregation process, assigning a fixed salinity to the sea ice, typical of multi-year ice. However, brine rejection is a dynamical, buoyancy-driven process and the salinity of sea ice varies significantly during the first growth season. As a result, current operational models may over predict the early brine fluxes from newly formed sea ice, which may have consequences for coupled simulations of the polar oceans. Improvements both in computational power and our understanding of the processes involved have led to the emergence of a new class of sea-ice models that treat brine rejection dynamically and should enhance predictions of the buoyancy forcing of the oceans.