We study the statistics of the viscous Burgers turbulence (BT) model, initialized at time t = 0 by a large class of Gaussian data. Using a first-principles analysis of the Hopf-Cole formula for the Burgers equation and the theory of large deviations for Gaussian processes, we characterize the tails of the probability distribution functions (PDFs) for the velocity u(x, t) and the velocity derivatives ∂nu(x,t)/∂xn,n = 1, 2, . . . . The PDF tails have a non-universal structure of the form log P(θ) ∝ -(Re)-ptqθr, where Re is the Reynolds number and p, q, and r depend on the order of differentiation and the infrared behavior of the initial energy spectrum.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics