Abstract
In this Letter we explore a new type of averaging in turbulence modelling, new types of characterization of the internal structure of turbulence (by two-point distribution function of fluid-particles), and consequences of the requirement that the Navier–Stokes equation and the governing equations of the models share a common structure of physical significance (Poisson structure). As a result we arrive at a turbulence model that includes the Reynolds-stress and LANS- α models, unifies them and extends them to models with an active advection.
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