Dynamics of shear instabilities near the ice-shelf–ocean interface

The melting of ice shelves into the ocean plays a major role, and is a key source of uncertainty, in sea level rise projections. Under-ice shelves, meltwater moves upslope, setting up a stratified shear flow with the warmer, but critically saltier, ocean beneath, regulating the transfer of heat between ice and the ambient ocean. Such features are incredibly difficult to access in situ , and so most research has focussed on the use of numerical modelling, laboratory experiments and analytical models to understand these processes, each with their own trade-offs. Here, novel numerical simulations of the Navier–Stokes equations approximate this flow for a tilted domain forced with fixed densities at the upper and lower boundaries to induce such a buoyant boundary shear current. These simulations and accompanying linear stability analysis (LSA) reveal that the shear flows under-ice shelves form a unique mixed-mode shear instability. This instability consists of paired Kelvin Helmholtz and Holmboe instabilities, highly effective at mixing the water column, and due to the restoring effect of the boundary forcing, results in a cyclical instability. The flow criticality is found to be well predicted by LSA, and dependent on diagnostic flow Reynolds and bulk Richardson numbers, whilst the local gradient Richardson number is not a useful indicator of instability in this problem. Based on these results, it is unclear how well this unusual route to turbulent mixing is represented in current models, highlighting the need for further investigation into turbulent heat transfer and ice-shelf melting.