STATISTICS OF DECAYING BURGERS TURBULENCE

Freely decaying Burgers turbulence at low and moderate Reynolds number R is studied by mapping closure and by numerical simulations. Good agreement is found for the single-point probability distribution function (pdf) of velocity gradient xi, for wave number spectra, and for various integral statistical quantities. The pdf of xi exhibits a nearly exponential tail at large negative xi, and a cusp with sharp cutoff at a positive value of xi. The pdf of fluid density has a power-law tail, so that high-order moments of density do not exist. Asymptotic analysis of the mapping closure as R --> infinity yields an inertial-range wave number spectrum of kinetic energy with the form E(k) is-proportional-to k-2. The pdf cusp becomes infinite as R --> infinity and gives rise to a flatness [xi4]/[xi2]2 is-proportional-to R in the limit.