Weakly nonlinear stability analysis of 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 propagation of a non-Newtonian, strain-rate-softening fluid representing ice that displaces a relatively inviscid and denser fluid that represents an ocean. Experimental observations show that rift patterns can emerge in such systems and that the number of rifts declines in time. A recent linear stability analysis predicts some of those observations. However, such a method is limited in predicting the strongly nonlinear evolution of the observed rift patterns. Our study focuses on the weakly nonlinear stability of such a system. We consider first a Newtonian fluid, and develop an amplitude equation that describes the time evolution of the perturbed fluid interface. We use this equation to explore the evolution of rift patterns and to develop more consistent predictions of the experimental system.