1994/09/06 by Sergei E. Esipov, Esipov, Sergei E.
Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9409023
33 pages, 2 by 2 figures are available upon request, PHYZZX Tex
arxiv created 1994/09/06 · arxiv updated 2009/11/30
For the problem of Burgers turbulence with random gaussian forcing a similarity functional solution of Hopf equation is presented and compared with scaling arguments and replica Bethe-anzatz treatments. The corresponding field theory is almost non-anomalous. In one dimension the local fluctuations develop self-similar time-dependent behavior, while relative fluctuations within the correlation length form a steady-state with gaussian distribution. This is the precise meaning of the so-called fluctuation-dissipation theorem. The one-dimensional properties are also studied numerically. It is shown that the fluctuation-dissipation theorem is invalid above one dimension and higher-order cumulants are non-zero. In two dimensions the cumulants exhibit logarithmic spatial dependence which is close to but different from that in the Edwards-Wilkinson case. No other similarity functional solution is found which may indicate that the ``strong-coupling'' results are not described by Burgers equation with gaussian noise.