Chapter 8: Implications for Everyday Systems

Section 4: Fluid Flow

Sound waves and shocks

Sound waves in a fluid correspond to periodic variations in density. The pictures below show how a density perturbation leads to a sound wave in a cellular automaton fluid. The sound wave turns out to travel at a fraction 1/Sqrt[2] of the microscopic particle speed.

When the speed of a fluid relative to an object becomes comparable to the speed of sound, the fluid will inevitably show variations in density. Typically shocks develop at the front and back of an object, as illustrated below.

It turns out that when two shocks meet, they usually have little effect on each other, and when there are boundaries, shocks are usually reflected in simple ways. The result of this is that in most situations patterns of shocks generated have a fairly simple geometrical structure, with none of the randomness of turbulence.

From Stephen Wolfram: A New Kind of Science [citation]