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Convection of microstructure and related problems. (English) Zbl 0622.76062
This paper is concerned with a particular homogenization of flows of viscous and inviscid fluid with rapidly varying structure in space and time. The appropriate averaged equations are obtained by a perturbation technique based on well-known multiple scale expansions of the field quantities which vary rapidly compared to spatial and temporal scales characterized by a small parameter. The cases of turbulent diffusion, eddy viscosity are considered as examples of transport by a random field.
The main analysis deals with solutions of Euler equations under rapidly varying initial data with stationary random components with mean zero. The averaged equations are found and their simple analytical and numerical solutions are discussed. There exist a number of misprints in the text which require special case from the part of the reader.
Reviewer: E.S.Suhubi

76F99 Turbulence
76R99 Diffusion and convection
76M99 Basic methods in fluid mechanics
35Q05 Euler-Poisson-Darboux equations
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