Universality in quasi-two-dimensional granular shock fronts above an intruder.

We experimentally study quasi-two-dimensional dilute granular flow around intruders whose shape, size, and relative impact speed are systematically varied. Direct measurement of the flow field reveals that three in-principle independent measurements of the nonuniformity of the flow field are in fact all linearly related: (1) granular temperature, (2) flow-field divergence, and (3) shear-strain rate. The shock front is defined as the local maxima in each of these measurements. The shape of the shock front is well described by an inverted catenary and is driven by the formation of a dynamic arch during steady flow. We find universality in the functional form of the shock front within the range of experimental values probed. Changing the intruder size, concavity, and impact speed only results in a scaling and shifting of the shock front. We independently measure the horizontal lift force on the intruder and find that it can be understood as a result of the interplay between the shock profile and the intruder shape.