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In this article we introduce a concept based on the differential constraints method to examine the closure procedure in Turbulence Models. We show how this concept may be applied to study the problem of interaction and mixing between two semi-infinite homogeneous turbulent flow fields of different scales.

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Introduction. New directions of turbulent-flow investigations based on constructing closed equations of turbulent transport and their numerical implementation on computers have been intensely developed lately. Tile approach based on the use of a two-parametric model of turbulence gained wide application, as well as second-order closure models, which are effective from the computational viewpoint and yield results whose accuracy is sufficient for many practical applications, ttowever, the use of these models for description of turbulent transport in stratified flows gives a qualitatively incorrect result in some cases (see, for example, [1]). The anisotropic character of the buoyancy effect on the structure of turbulence is manifested in the long-wave range of the spectrum of turbulent oscillations [2]. This spectral range corresponds to large-scale vortex structures (LVS) containing the main portion of turbulence energy. According to experimental and theoretical studies, the following LVS are formed in stratified flows: turbulent spots in the case of stable stratification and coherent structures in the case of unstable stratification, which are mainly responsible for turbulent transport. The effects of intermittency and asymmetry of vertical turbulent transport caused by the influence of LVS make the probability distributions of turbulent fluctuations significantly non-Gaussian. The turbulence structure in these flows is usually described by third-order closure models, where the triple correlations (asymmetry) are calculated from differential transport equations (sec, for example, [3, 4]). A refinement of such models is proposed in the present paper.Applicability of Millionshchikov's Quasinormality Hypothesis. Millionshchikov's quasinormality hypothesis for calculation of the fourth moments of statistical characteristics of turbulent flows .(velocity fluctuations and mixed fourth-order covariations of velocity, temperature, and concentration fluctuations) is often used for closure in constructing semi-empirical models of turbulent transport of the second and third order. According to this hypothesis, fourth-order cumulants can be ignored in comparison with the corresponding correlation functions. As applied to the moments of hydrodynamic fields, this hypothesis means that we can use the equality that expresses the fourth moments through the second moments