Andrew Wells

Abstract:

Around Greenland, the transport of heat and fresh meltwater between the ocean and Greenland's Ice Sheet is mediated by circulation in several hundred proglacial fjords. These fjords are long and narrow, with circulation controlled by a variety of processes. This circulation, and the resultant heat transported to the ice sheet has global implications. However, the spatial scales of these fjords means that they cannot be directly represented in global scale climate models, as currently achievable horizontal resolutions are too coarse to resolve fjords directly. Therefore, a subgrid-scale parameterization scheme is required, to include the impact of fjord circulation on Greenland's Ice Sheet in these models. The development of such a scheme requires increased theoretical understanding, with the aim of capturing the circulation response simply, over a relevant range of the parameter space.

Current climate models add freshwater runoff from Greenland's Ice Sheet into the ocean model in the surface grid cell, and do not account for the impacts of fjord circulation on melt rates at glacial termini. Therefore, we focus on predicting the depth at which fresh meltwater enters the wider ocean, and the flow structure at the ice face itself, to understand the feedback on ice melt rates. We consider a subglacial discharge driven regime, with a localised source of subglacial discharge into the fjord at the glacial grounding line. We employ a combination of computational modelling using idealised configurations in MITgcm, and theoretical explorations, to capture this circulation as simply as possible. For fjords without sills, we find that the cross-fjord integrated velocity profile at the fjord mouth echoes that at the ice face. Further, we find that a horizontal recirculation cell develops at the ice face, as the fjord responds to horizontal velocities driven by the plume itself, generating flow across the entire ice face. We use scaling laws previously developed for turbulent plumes to provide a simple prediction of the cross-fjord integrated velocity structure at the fjord mouth, predicting the depth level at which meltwater enters the wider ocean. We develop theoretical predictions for the cross-fjord flow at the ice face, as a consequence of the flow directly induced by a buoyant plume and the circulation response in the fjord, allowing prediction of the pattern of melt across the ice face.

Abstract:

We use well resolved numerical simulations with the Lattice Boltzmann Method to study Rayleigh-B´enard convection in cells with a fractal boundary in two dimensions for P r = 1 and Ra ∈ [10^7 , 10^10]. The fractal boundaries are functions characterized by power spectral densities S(k) that decay with wavenumber, k, as S(k) ∼ k^p (p < 0). The degree of roughness is quantified by the exponent p with p < −3 for smooth (differentiable) surfaces and −3 ≤ p < −1 for rough surfaces with Hausdorff dimension D_f =1/2 (p + 5). By computing the exponent β in power law fits Nu ∼ Ra^β, where Nu and Ra are the Nusselt and the Rayleigh numbers for Ra ∈ [10^8, 10^10], we observe that heat transport scaling increases with roughness over the top two decades of Ra ∈ [10^8, 10^10]. For p = −3.0, −2.0 and −1.5 we find β = 0.288 ± 0.005, 0.329 ± 0.006 and 0.352 ± 0.011, respectively. We also observe that the Reynolds number, Re, scales as Re ∼ Ra^ξ , where ξ ≈ 0.57 over Ra ∈ [10^7, 10^10], for all p used in the study. For a given value of p, the averaged Nu and Re are insensitive to the specific realization of the roughness.

Abstract:

Thermodynamic ablation of ice in contact with the ocean is an essential element of ice sheet and ocean interactions but is challenging to model and quantify. Building on earlier observations of sea ice ablation, a variety of recent theoretical, experimental and observational studies have considered ice ablation in contrasting geometries, from vertical to near-horizontal ice faces, and reveal different scaling behaviour for predicted ablation rates in different dynamical regimes. However, uncertainties remain about when the contrasting results should be applied, as existing model parameterisations do not capture all relevant regimes of ice–ocean ablation. To progress towards improved models of ice–ocean​ interaction, we synthesise current understanding into a classification of ablation types. We examine the effect of the classification on the parameterisation of turbulent fluxes from the ocean towards the ice, and identify the dominant processes next to ice interfaces of different orientation. Four ablation types are defined: melting and dissolving based on ocean temperatures, and shear-controlled and buoyancy-controlled regimes based on the dynamics of the near-ice molecular sublayer. We describe existing observational and modelling studies of sea ice, ice shelves, and glacier termini, as well as laboratory studies, to show how they fit into this classification. Two sets of observations from the Ross and Ronne Ice Shelf cavities suggest that both the buoyancy-controlled and shear-controlled regimes may be relevant under different oceanographic conditions. Overall, buoyancy-controlled dynamics are more likely when the molecular sublayer has lower Reynolds number, and shear for higher Reynolds number, although the observations suggest some variability about this trend.