Popping, splitting and merging tongues in radially spreading extensional flows

Floating ice shelves can undergo severe failure, in which fractures evolve into deep rifts that lead to the calving of ice bergs. Fluid mechanically such systems are analogue to extensional flows of non-Newtonian fluids with strain-rate-softening viscosity, having freely moving fluid fronts. Similar flows in circular geometry with a single moving front undergo an instability in which circular fronts evolves into rift-finger patterns having a dominant wavelength that declines in time.

Here we explore similar flows but with an inner moving front in addition to an outer moving front. The patterns that emerge in laboratory experiments consist of floating tongues that can form through popping in between existing tongues or through splitting of existing tongues, as well as tongues that undergo merging with neighboring tongues. We describe the evolution of these patterns and identify quantities that control each of the operating mechanisms and their interactions.