"Nearly perfect flows" by Wendy Zhang

In school, we learned that fluid flow becomes simple in two limits.  Over long lengthscales and at high speeds, inertia dominates and the motion can approach that of a perfect fluid with zero viscosity.  On short lengthscales and at slow speeds, viscous dissipation is important.  Fluid flows that correspond to the formation of a finite-time singularity in the continuum description involve both a vanishing characteristic lengthscale and a diverging velocity scale.  These flows can therefore evolve into final limits that defy expectations derived from properties of their initial states.  This talk focuses on 3 familiar processes that belong in this category: the formation of a splash after a liquid drop collides with a dry solid surface, the emergence of a highly-collimated sheet from the impact of a jet of densely-packed, dry grains, and the pinch-off of an underwater bubble.  In all three cases, the motion is dominated by inertia but a small amount of dissipation is also present.  Our works show that dissipation is important for the onset of splash, plays a minor role in the ejecta sheet formation after jet impact, but becomes irrelevant in the break-up of an underwater bubble.  An important consequence of this evolution towards perfect-fluid flow is that deviations from cylindrical symmetry in the initial stages of pinch-off are not erased by the dynamics.  Theory, simulation and experiment show detailed memories of initial imperfections remain encoded, eventually controlling the mode of break-up.  In short, the final outcome is not controlled by a single universal singularity but instead displays an infinite variety.