Universal functions for Burgers turbulence

For the steady state of Burgers turbulence, Saffman [in Topics in Nonlinear Physics (Springer, Berlin, 1968), pp. 485???614] derived analytical expressions for the second-order structure function and energy spectrum in the inertial-dissipation range. By nondimensionalizing these quantities, we derive universal functions for the structure function and the energy spectrum and flux. We simulate Burgers turbulence with large-scale forcing for various injection rates and viscosity. For all these runs, the nondimensionalized structure functions and the energy spectra and fluxes collapse to the respective universal functions.