Nonlinear regime of radially spreading extensional flows and ice shelves

Ice shelves that spread into the ocean can develop rifts, which can trigger ice-berg calving and enhance ocean-induced melting. Fluid mechanically, this system is analogous to the radial propagation of a non-Newtonian, strain-rate- softening fluid (ice) that displaces a relatively inviscid and denser fluid (ocean). Laboratory experiments showed that rift patterns can emerge in such systems and that the number of rifts declines in time. Theoretically, linear-stability analysis predicts that shear-tinning fluids can be unstable and potentially develop rifts, while Newtonian fluids are always stable. Quasi-3D numerical simulation of the full non-linear model that accounts for nonuniform thickness has confirmed that Newtonian fluids are globally stable, while they can evolve non-axisymmetric patterns having cusps that were not predicted theoretically.

Here we extend the numerical simulations to explore the nonlinear regime of radially spreading extensional flows of shear-thinning fluids. We show that a sufficiently shear-thinning fluid become unstable, developing tearing patterns reminiscent to those observed experimentally. Such patterns can emerge from monochromatic perturbations regardless of their amplitudes. We analyse the patterns emerging as a function of the flow properties and initial perturbation, and discuss the mechanism underlying the formation of rifts.