Mean-Field Burgers' Model of Turbulence
Brown University Dept of Physics Report BROWN-HET-516
A mean-field expansion of the Martin, Siggia, and Rose functional formalism for turbulence is proposed as a "strong-coupling" approximation. To carry out the expansion, the volume of the wavenumber space must be truncated to a large but finite amount. Burgers' model with homogeneous average flow is examined in detail to several orders of approximation. The two point cumulant is calculated. The mean-field expansion is described as a perturbation expansion, with its small parameter inversely proportional to the truncated volume of wavenumber space. Renormalization and some features of the expansion are explored.