Multifractality in the stochastic Burgers equation

We investigate numerically the scaling properties of spatiotemporal correlation functions in the one-dimensional Burgers equation driven by noise with variance proportional to |k${\mathrm{|}}^{\mathrm{\beta }}$. The long-distance behavior at β<0 is determined by shocks that lead to multifractality in the high-order structure functions and a dynamical exponent z close to unity. For β>0 earlier theoretical predictions for scaling exponents constrained by Galilean invariance obtain; these results are not expected to hold for β<0. Nevertheless, the continuation of the fixed point to β<0 correctly predicts some of the properties, an occurrence that we relate to the anomalous scaling of composite operators. © 1996 The American Physical Society.