arXiv subjects

David W. Rees Jones

Publications and source records attributed to David W. Rees Jones.

8 recordsLinked to original sources

arXiv2026

Resonant lunar tides of Earth's core and basal magma ocean

Earth's magnetic field is generated by fluid motion in the liquid-metal core and has been active for billions of year. However, prior to the onset of inner-core growth, the sources of mechanical power that drove the geodynamo remain uncertain. During this period, the core may have been overlain by a basal magma ocean (BMO), creating two immiscible fluid layers separated by a density interface, beneath the solid mantle. We develop a theory for lunar tides in this core--BMO system, in which the tidal potential acts on the density contrast between the two layers rather than through deformation of a bounding envelope. The resulting dynamics differ fundamentally from previous models of tidally driven core flow. In the inviscid limit, the response transitions from an equilibrium tide to an inertia--self-gravity wave as forcing frequency increases. The two regimes are separated by a resonance that occurs when the forcing frequency matches the natural frequency of the interfacial mode. The inviscid core flow is formally identical to the canonical elliptical vortex, linking the problem to the theory of elliptical instability. Finite viscosity regularises the resonance, introduces phase lag and generates oscillatory boundary layers. Combined with parameterised models of lunar recession and BMO crystallisation, the theory predicts enhanced core-boundary ellipticity, core-flow speed, magnetic Reynolds number and instability metrics, particularly near resonance. These results identify a previously unexplored mechanism for tidally driven flow in differentiated planetary bodies and show that a BMO can enhance tidal coupling to the core, potentially contributing to dynamo action.

physics.geo-ph↗

arXiv2025

Thermodynamic growth of sea ice: assessing the role of salinity using a quasi-static modelling framework

Sea ice is a mushy layer, a porous material whose properties depend on the relative proportions of solid and liquid. The growth of sea ice is governed by heat transfer through the ice together with appropriate boundary conditions at the interfaces with the atmosphere and ocean. The salinity of sea ice has a large effect on its thermal properties so might naively be expected to have a large effect on its growth rate. However, previous studies observed a low sensitivity throughout the winter growth season. The goal of this study is to identify the controlling physical mechanisms that explain this observation. We develop a simplified quasi-static framework by applying a similarity transformation to the underlying heat equation and neglecting the explicit time dependence. We find three key processes controlling the sensitivity of growth rate to salinity. First, the trade-off between thermal conductivity and (latent) heat capacity leads to low sensitivity to salinity even at moderately high salinity and brine volume fraction. Second, the feedback on the temperature profile reduces the sensitivity relative to models that assume a linear profile, such as zero-layer Semtner models. Third, thicker ice has the opposite sensitivity of growth rate to salinity compared to thinner ice, sensitivities that counteract each other as the ice grows. Beyond its use in diagnosing these sensitivities, we show that the quasi-static approach offers a valuable sea-ice model of intermediate complexity between zero-layer Semtner models and full partial-differential-equation-based models such as Maykut-Untersteiner/Bitz-Lipscomb and mushy-layer models.

physics.ao-ph↗

arXiv2021

Magmatic channelisation by reactive and shear-driven instabilities at mid-ocean ridges: a combined analysis

It is generally accepted that melt extraction from the mantle at mid-ocean ridges (MORs) is concentrated in narrow regions of elevated melt fraction called channels. Two feedback mechanisms have been proposed to explain why these channels grow by linear instability: shear flow of partially molten mantle and reactive flow of the ascending magma. These two mechanisms have been studied extensively, in isolation from each other, through theory and laboratory experiments as well as field and geophysical observations. Here, we develop a consistent theory that accounts for both proposed mechanisms and allows us to weigh their relative contributions. We show that interaction of the two feedback mechanisms is insignificant and that the total linear growth rate of channels is well-approximated by summing their independent growth rates. Furthermore, we explain how their competition is governed by the orientation of channels with respect to gravity and mantle shear. By itself, analysis of the reaction-infiltration instability predicts the formation of tube-shaped channels. We show that with the addition of even a small amount of extension in the horizontal, the combined instability favours tabular channels, consistent with the observed morphology of dunite bodies in ophiolites. We apply the new theory to MORs by calculating the accumulated growth and rotation of channels along streamlines of the solid flow. We show that reactive flow is the dominant mechanism deep beneath the ridge axis, where the most unstable orientation of high-porosity channels is sub-vertical. Channels are then rotated by the solid flow away from the vertical. The contribution of the shear-driven instability is confined to the margins of the melting region. Within the limitations of our study, the shear-driven feedback is not responsible for significant melt focusing or for shallowly dipping seismic anisotropy [abridged].

physics.geo-ph↗

arXiv2020

Fast magma ascent, revised estimates from the deglaciation of Iceland

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.

physics.geo-ph↗

arXiv2019

Consequences of glacial cycles for magmatism and carbon transport at mid-ocean ridges

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.

physics.geo-ph↗

arXiv2019

Reaction-infiltration instability in a compacting porous medium

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.

physics.flu-dyn↗

arXiv2017

Thermal impact of magmatism in subduction zones

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.

physics.geo-ph↗

arXiv2015

The solidification of a disk-shaped crystal from a weakly supercooled binary melt

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.

cond-mat.mtrl-sci↗