Statistical modeling of Burgers turbulence with a superposition of characteristic functionals

We study an ensemble of random fields, each with statistics described by a general characteristic functional. The typical length scale of these fields is a random variable and is used to model intermittency. This ensemble decomposition approach [Wilczek, New J. Phys. 18, 125009 (2016)] allows for an analytically tractable approximation to turbulent statistics, and is applied to the Burgers equation. By choosing smooth correlation functions and an appropriate distribution for the typical length scale, we build a description of Burgers turbulence at an infinite Reynolds number, in which the velocity statistics are Gaussian, but increment statistics are bifractal. Skewness, a hallmark of turbulent fields, is obtained by truncating a Taylor expanded cumulant generating functional, and this is shown to be a useful approximation.