,

where is the spatial coordinate, is time, and is some conserved physical quantity. In Burgers turbulence (or "burgulence"), Burgers's equation is considered to be a stochastic partial differential equation whose solution reveals some aspects of turbulent behavior in fluid flow. In this Demonstration, Burgers's equation is solved with random initial conditions (i.e., a randomly perturbed Gaussian waveform) as a model of turbulence. The left-hand plot shows the time evolution of the waveform, while the right-hand plot shows the time evolution of the -density function (i.e., the distribution of -values at times ). The range of (i.e., [0,1]) is broken into 20 intervals. Three turbulence levels can be tested: low, medium, and high.

Since Burgers's equation is a flux-conservative hyperbolic partial differential equation, it is amenable to finite-volume methods. In this Demonstration, Burgers's equation is solved with the Harten–Lax–van Leer (HLL) method with periodic boundary conditions.