It actually IS a step function. A shock wave by definition is an instantaneous change in fluid properties. At the molecular level, the change in properties is o

It actually IS a step function. A shock wave by definition is an instantaneous change in fluid properties. At the molecular level, the change in properties is observed as occurring within a mean free path length (average distance a gas molecule travels before colliding). Imaging that shows the jump: https://phys.org/news/2015-08-schlieren-images-reveal-supersonic.html https://phys.org/news/2015-08-schlieren-images-reveal-supers...