Stability 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 representing ice that displaces a relatively inviscid and denser fluid that represents an ocean. Laboratory experiments showed that rift patterns can emerge in such systems and that the number of rifts declines in time. Such a dynamics was confirmed theoretically, but only for the earlier stage of the flow and for a fluid layer of uniform thickness. We investigate numerically the stability and late-time evolution of radially spreading, axisymmetric fluid layer of non-uniform thickness. We validate the two dimensional finite-element Úa model using similarity solutions of radially spreading layers of Newtonian fluid that were found consistent with laboratory experiments. We then explore the stability of the flow by introducing geometric perturbations to the initial front and tracing their evolution. Our simulations show that the front of Newtonian fluids is stable, though memory of the perturbation spectral form persists.