Publications by Andrew Wells

Solidification of binary aqueous solutions under periodic cooling. Part 1. Dynamics of mushy-layer growth


G-Y Ding, AJ Wells, J-Q Zhong

Solidification of binary aqueous solutions under periodic cooling. Part 2. Distribution of solid fraction


G-Y Ding, AJ Wells, J-Q Zhong

Mushy-layer growth and convection, with application to sea ice.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 377 (2019) 20180165-

AJ Wells, JR Hitchen, JRG Parkinson

Sea ice is a reactive porous medium of ice crystals and liquid brine, which is an example of a mushy layer. The phase behaviour of sea ice controls the evolving material properties and fluid transport through the porous ice, with consequences for ice growth, brine drainage from the ice to provide buoyancy fluxes for the polar oceans, and sea-ice biogeochemistry. We review work on the growth of mushy layers and convective flows driven by density gradients in the interstitial fluid. After introducing the fundamentals of mushy-layer theory, we discuss the effective thermal properties, including the impact of salt transport on mushy-layer growth. We present a simplified model for diffusively controlled growth of mushy layers with modest cooling versus the solutal freezing-point depression. For growth from a cold isothermal boundary, salt diffusion modifies mushy-layer growth by around 5-20% depending on the far-field temperature and salinity. We also review work on the onset, spatial localization and nonlinear development of convective flows in mushy layers, highlighting recent work on transient solidification and models of nonlinear convection with dissolved solid-free brine channels. Finally, future research opportunities are identified, motivated by geophysical observations of ice growth. This article is part of the theme issue 'The physics and chemistry of ice: scaffolding across scales, from the viability of life to the formation of planets'.

Salinity Control of Thermal Evolution of Late Summer Melt Ponds on Arctic Sea Ice


J-H Kim, W Moon, AJ Wells, JP Wilkinson, T Langton, B Hwang, MA Granskog, DWR Jones

Frazil-ice growth rate and dynamics in mixed layers and sub-ice-shelf plumes

CRYOSPHERE 12 (2018) 25-38

DWR Jones, AJ Wells

Frazil-ice growth rate and dynamics in mixed layers and sub-ice-shelf plumes

The Cryosphere Discussions Copernicus GmbH (0) 1-22

DW Rees Jones, AJ Wells

<jats:p>The growth of frazil or granular ice is an important mode of ice formation in the cryosphere. Recent advances have improved our understanding of the microphysical processes that control the rate of ice-crystal growth when water is cooled beneath its freezing temperature. These advances suggest that crystals grow much faster than previously thought. In this paper, we consider models of a population of ice crystals with different sizes to provide insight into the treatment of frazil ice in large-scale models. We consider the role of crystal growth alongside the other physical processes that determine the dynamics of frazil ice. We apply our model to a simple mixed layer (such as at the surface of the ocean) and to a buoyant plume under a floating ice shelf. We provide numerical calculations and scaling arguments to predict the occurrence of frazil-ice explosions, which we show are controlled by crystal growth, nucleation and, gravitational removal. Faster crystal growth, higher secondary nucleation and slower gravitational removal make frazil-ice explosions more likely. We identify steady-state crystal size distributions, which are largely insensitive to crystal growth rate but are affected by the relative importance of secondary nucleation to gravitational removal. Finally, we show that the fate of plumes underneath ice shelves is dramatically affected by frazil-ice dynamics. Differences in the parameterization of crystal growth and nucleation give rise to radically different predictions of basal accretion and plume dynamics; and can even impact whether a plume reaches the end of the ice shelf or intrudes at depth. </jats:p>

Turbulent plumes from a glacier terminus melting in a stratified ocean


SJ Magorrian, AJ Wells

The impact of imperfect heat transfer on the convective instability of a thermal boundary layer in a porous media


J Hitchen, AJ Wells

Solidification of a disk-shaped crystal from a weakly supercooled binary melt.

Physical review. E, Statistical, nonlinear, and soft matter physics 92 (2015) 022406-

DW Rees Jones, AJ Wells

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 vapor 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 the salt rejected at the growing interface are significant. Our calculations demonstrate that certain previous parametrizations, based on scaling arguments, substantially underestimate crystal growth rates by a factor of order 10-100 for low aspect ratio disks, and we provide a parametrization for use in models of ice crystal growth in environmental settings.

Channelization of plumes beneath ice shelves


MC Dallaston, IJ Hewitt, AJ Wells

Steady turbulent density currents on a slope in a rotating fluid


GE Manucharyan, W Moon, F Sevellec, AJ Wells, J-Q Zhong, JS Wettlaufer

Nonlinear mushy-layer convection with chimneys: stability and optimal solute fluxes


AJ Wells, JS Wettlaufer, SA Orszag

Finite-sample-size effects on convection in mushy layers


J-Q Zhong, AT Fragoso, AJ Wells, JS Wettlaufer

Mushy-layer dynamics in micro and hyper gravity

Physics of Fluids 24 (2012)

JG O'Rourke, AJE Riggs, CA Guertler, PW Miller, CM Padhi, MM Popelka, AJ Wells, AC West, JQ Zhong, JS Wettlaufer

We describe the results of experiments on mushy layers grown from aqueous ammonium chloride solution in normal, micro, and hyper gravity environments. In the fully developed chimney state, the chimney plume dynamics differ strikingly when conditions change from micro to hyper gravity. In microgravity, we find fully arrested plume motion and suppressed convection. As gravity exceeds Earth conditions, we observe a host of phenomena, ranging from arched plumes that undergo forced Rayleigh-Taylor instabilities to in-phase multiple plume oscillatory behavior. For the same initial solute concentrations and fixed boundary cooling temperatures, we find that, in runs of over two hours, the averaged effects of microgravity and hypergravity result in suppressed growth of the mushy layers, a phenomenon caused by a net enhancement of convective heat and solute transport from the liquid to the mushy layers. These behaviors are placed in the context of the theory of convecting mushy layers as studied under normal laboratory conditions. © 2012 American Institute of Physics.

Melting and dissolving of a vertical solid surface with laminar compositional convection


AJ Wells, MG Worster

Brine fluxes from growing sea ice


AJ Wells, JS Wettlaufer, SA Orszag

Maximal Potential Energy Transport: A Variational Principle for Solidification Problems


AJ Wells, JS Wettlaufer, SA Orszag

Variations in Ocean Surface Temperature due to Near-Surface Flow: Straining the Cool Skin Layer


AJ Wells, C Cenedese, JT Farrar, CJ Zappa

A geophysical-scale model of vertical natural convection boundary layers

Journal of Fluid Mechanics 609 (2008) 111-137

AJ Wells, MG Worster

A model is developed for turbulent natural convection in boundary layers formed next to isothermal vertical surfaces. A scaling analysis shows that the flow can be described by plume equations for an outer turbulent region coupled to a resolved near-wall laminar flow. On the laboratory scale, the inner layer is dominated by its own buoyancy and the Nusselt number scales as the one-third power of the Rayleigh number (Nu ∝ Raz1/3). This gives a constant heat flux, consistent with previous experimental and theoretical studies. On larger geophysical scales the buoyancy is strongest in the outer layer and the laminar layer is driven by the shear imposed on it. The predicted heat transfer correlation then has the Nusselt number proportional to the one-half power of Rayleigh number (Nu ∝ Raz1/2) so that a larger heat flux is predicted than might be expected from an extrapolation of laboratory-scale results. The criteria for transitions between flow regimes are consistent with a hierarchy of instabilities of the near-wall laminar flow, with a buoyancy-driven instability operating on the laboratory scale and a shear-driven instability operating on geophysical scales. © 2008 Cambridge University Press.

Optimal and hysteretic fluxes in alloy solidification: Variational principles and chimney spacing

arXiv (0)

AJ Wells, JS Wettlaufer, SA Orszag

We take a numerical approach to analyze the mechanisms controlling the spacing of chimneys -- channels devoid of solid -- in two-dimensional mushy layers formed by solidifying a binary alloy. Chimneys are the principal conduits through which buoyancy effects transport material out of the mushy layer and into the liquid from which it formed. Experiments show a coarsening of chimney spacing and we pursue the hypothesis that this observation is a consequence of a variational principle: the chimney spacing adjusts to optimize material transport and hence maximize the rate of removal of potential energy stored in the mushy layer. The optimal solute flux increases approximately linearly with the mushy layer Rayleigh number. However, for spacings below a critical value the chimneys collapse and solute fluxes cease, revealing a hysteresis between chimney convection and no flow.