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We construct anisotropoviscous two-and three-layer models of the effect of reduction of hydrodynamic resistance through the addition of polymers. The three-layer model can be used to compute the hydrodynamic resistance of turbulent flows with polymer additives in the entire region of variation of the Reynolds numbers, and the two-dimensional model can be used with large Reynolds numbers. Two figures. Bibliography: 3 titles.The second author [1] has constructed a semiempirical theory of the effect of reduction of hydrodynamic resistance through the addition of polymers in the context of a structural approach. The basis of the theory is the mechanism of resonance absorption of turbulent energy of macromolecules of polymers. Here at each point of the flow a symmetric tensor of rank two #ij is prescribed, whose components have the dimension of dynamic viscosity. In the present article, by introducing the averaged two-and three-layer models of the flow of a fluid with polymer additives, we simplify the basic relations obtained in [1]. For a two-dimensional flow the longitudinal component #zz (in the direction of flow) and the transverse component #22 of the tensor, in terms of which the coefficient of anisotropy of dynamic viscosity A = #22/#11 is computed, are decisive. For such a flow [1] A = 1 + fz (c, M, 7)f2(w2, t.~l, N, c), (i) where ~tT fz = 0.188arctan(0.166cM~ f2 = 12 ~ 1_ arctan (w2/wz -1)p (2) ~r p=l p ~2/Wl + p2 ,c is the concentration; M is the molecular mass of the polymer; -7 is a parameter that takes account of the distention of the polymer molecules; w2 = w2(y) is the distribution of the frequencies of the Kolmogorov perturbations over a section of the turbulent flow under consideration; ~1 = wl(y) is the distribution of the analogous frequencies at the threshold Reynolds number; N is the number of segments in the molecular chain; and ~ is a parameter that characterizes the distribution of relaxation times in the spectrum of the polymer molecule. Using relation (1), we can construct a nonlayer model of turbulence near a wall [1], which makes it possible to compute the profile of the average velocity and hydrodynamic resistance in turbulent flows with polymer additives, including the maximal (limiting) reduction of resistance. However, in order to obtain simpler relations in the applied computations it makes sense to construct averaged two-and three-layer models of the flow of fluids with polymer additives. For these models the average coefficient of anisotropy of the dynamic viscosity A can be introduced, and in the expression for the function f2 one can pass to the ratio of the averaged frequencies ~2/~1. 1 rl(y) dy averaged over the section of the Consider the integral Kolmogorov turbulence scale f/= c~ flow and the frequency ~ = klV/~? 2 corresponding to it [2], where a is the width of the flow, and kl is a constant of the order of 1. For these quantities we have = z (3)

The article deals with the growing problem of training personnel for the new economy and social life in Russia, focused on achieving sustainable development of urban areas. We consider the main directions of training future specialists in the field of urban development, relying on the Russian and world experiences.

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