Statistical properties of solutions of the random-force–driven Burgers equation are investigated by use of the dynamic renormalization group and direct numerical simulations. The agreement between computed and analytical results on both exponents and amplitudes of the correlation functions is good. It is shown that a small-scale noise dominates large-scale, long-time (k→0,ω→0) behavior of the system and, as a consequence, no microscopic system of interacting particles described by Burgers equation in the hydrodynamic limit (k→0,ω→0) exists.

• Received 4 January 1988

DOI:https://doi.org/10.1103/PhysRevLett.60.1840