Statistical Modeling of Bifractal Statistics with a Superposition of Characteristic Functionals

Abstract Turbulent fields display intermittent and skewed observables as some of their main features, but translating them to multipoint statistics remains a challenge. This work constructs a pseudo-characteristic functional inspired by the statistics of the one-dimensional Burgers velocity field. The functional is chosen as an ensemble of nearly Gaussian basis functionals with fluctuating typical scales, and the distribution of the fluctuating scale is such that one-point velocity statistics are Gaussian, while increments and gradients show bifractal statistics. This behavior can be obtained from the asymptotic properties of the base and scale distributions. Skewness is added with a functional Taylor expansion and truncation of a characteristic functional, producing statistics compatible with the Burgers analog of the 4/5 law.