Statistical closures from the Martin-Siggia and Rose approach to turbulence

Abstract

The goal of this paper is to study the statistical closures suggested by the Martin-Siggia and Rose approach to statistical turbulence. We find that the formalism leads to a Bethe-Salpeter equation for the three point correlation of the velocity field. In the leading order approximation this equation becomes an explicit expression. We discuss under which approximations this closure reduces to that proposed in W D McComb and S R Yoffe, A formal derivation of the local energy transfer (LET) theory of homogeneous turbulence, J. Phys. A: Math. Theor. 50, 375501 (2017). This suggests ways to improve upon this closure by dropping these restrictions, resumming the perturbative expansion and/or applying renormalization group techniques.