The dynamics of velocity fluctuations, governed by the one-dimensional Burgers equation, driven by a white-in-time random force with the spatial spectrum $\overline{ |f(k)|^2}\proptok^{ -1}$, is considered. High-resolution numerical experiments conducted in this work give the energy spectrum $E(k)\propto k^{ -\beta}$ with $\beta =5/3\pm 0.02$. The observed two-point correlation function $C(k,\omega)$ reveals $\omega\propto k^z$ with the "dynamical exponent" $z\approx 2/3$. High-order moments of velocity differences show strong intermittency and are dominated by powerful large-scale shocks. The results are compared with predictions of the one-loop renormalized perturbation expansion.
Categories: adap-org nlin.AO