The Vertical Structure and Entrainment of Subglacial Melt Water Plumes

Abstract

Basal melting of marine‐terminating glaciers, through its impact on the forces that control the flow of the glaciers, is one of the major factors determining sea level rise in a world of global warming. Detailed quantitative understanding of dynamic and thermodynamic processes in melt‐water plumes underneath the ice‐ocean interface is essential for calculating the subglacial melt rate. The aim of this study is therefore to develop a numerical model of high spatial and process resolution to consistently reproduce the transports of heat and salt from the ambient water across the plume into the glacial ice. Based on boundary layer relations for momentum and tracers, stationary analytical solutions for the vertical structure of subglacial non‐rotational plumes are derived, including entrainment at the plume base. These solutions are used to develop and test convergent numerical formulations for the momentum and tracer fluxes across the ice‐ocean interface. After implementation of these formulations into a water‐column model coupled to a second‐moment turbulence closure model, simulations of a transient rotational subglacial plume are performed. The simulated entrainment rate of ambient water entering the plume at its base is compared to existing entrainment parameterizations based on bulk properties of the plume. A sensitivity study with variations of interfacial slope, interfacial roughness and ambient water temperature reveals substantial performance differences between these bulk formulations. An existing entrainment parameterization based on the Froude number and the Ekman number proves to have the highest predictive skill. Recalibration to subglacial plumes using a variable drag coefficient further improves its performance.

Ice Shelf Basal Melt Sensitivity to Tide‐Induced Mixing Based on the Theory of Subglacial Plumes

“…While improving the representation of turbulent fluxes at the ice‐ocean interface has been the focus of many recent modeling and observational studies (e.g., Dansereau & Losch, 2013; Rosevear et al., 2022), the processes controlling the vertical transport of heat from the ambient waters into the boundary current are not yet well understood. For models in which turbulent mixing across the pycnocline is unresolved, like the plume model employed in this study, this uncertainty means that the representation of the entrainment process relies on choosing between one of many proposed parameterizations that each vary substantially in terms of predicted entrainment rates (Burchard et al., 2022). More sophisticated 3‐D ocean models with sufficiently high resolution may not depend on entrainment parameterizations, but they typically employ generic vertical mixing schemes that are not necessarily accurate for the sub‐ice shelf environment and that may respond differently to the addition of tides.…”

High‐Resolution Simulations of the Plume Dynamics in an Idealized 79°N Glacier Cavity Using Adaptive Vertical Coordinates

“…Without a well‐preserved plume, an analysis of the entrainment rate as shown in Figure 6 would not be feasible. An insufficient representation of the plume development has also implications on the accuracy of the computation of basal melt rates (Burchard et al., 2022). Furthermore, a good simulation of meltwater export from the fjord into the open ocean demands a good preservation of the plume properties with minimal spurious mixing.…”

“…We want to diagnose the bulk values following the ideas by Arneborg et al. (2007) in the modified form for plumes under ice shelves (Burchard et al., 2022): $$$\bar{b}D=\int \nolimits_{-\infty }^{\eta }b(z)\,\mathrm{d}z,$$$ $$$\bar{b}{D}^{2}=2\int \nolimits_{-\infty }^{\eta }b(z){z}^{\prime }\,\mathrm{d}z,$$$ $$$\bar{u}D=\int \nolimits_{-\infty }^{\eta }u(z)\,\mathrm{d}z,$$$ where z ′ = η − z is the distance from the ice–ocean interface η , b ( z ) = − g [ ρ ( z ) − ρ 0 ]/ ρ 0 is the buoyancy, and ρ 0 is the ambient ocean density. However, the above equations have been derived in a 1D setting with the assumptions that the ambient water below the plume is homogeneous (with density ρ 0 ) and stagnant ( u = 0), which is not the case in our 2D model.…”

“…To analyze the entrainment of the subglacial plume, we compute its bulk properties, that is, the vertically averaged plume characteristics, in particular the plume thickness D, its buoyancy 𝐴𝐴 b𝑏 , and its velocity 𝐴𝐴 𝐴 𝐴𝐴 . We want to diagnose the bulk values following the ideas by Arneborg et al (2007) in the modified form for plumes under ice shelves (Burchard et al, 2022):…”

“…which means that the plume thickness increases in x-direction by flow convergence 𝐴𝐴 (−𝐷𝐷𝐷𝐷𝑥𝑥 ū𝑢) , melting, and entrainment (Jenkins, 1991). Since the melting is computed by our numerical model, we can reformulate (10) to diagnose the entrainment (Burchard et al, 2022):…”