Model of fourth-order cumulants for description of turbulent transport by large-scale vortex structures

A model for calculation of fourth-order cumulants is presented. Based on the Schwarz inequalities, a dependence between the coefficients of the model is established, which allows one to determine their numerical values. The use of an algebraic version of the model for parametrization of the process of turbulent diffusion in transport equations for third-order correlations does not require additional empirical information and offers a correct description of turbulent transport by large-scale vortex structures. Millionshchikov’s hypothesis turns out to be insufficient for that.