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In the eighties, thanks to progress in computational mathematics and the appearance of supercomputers, it seemed that the problems of turbulence would soon be solved either by direct numerical solution of the complete Navier--Stokes equations or by large-scale modeling (solution of the filtered Navier--Stokes equations). For a series of reasons (impossibility of assigning the initial data, nonuniversality of the small-scale part of the spectrum of turbulence, etc.) these hopes were not realized. Now, as before, differential turbulence models are the main tool for solving problems of complex turbulent flow. This applies especially to engineering problems, where the possibility of carrying out a large volume of computations in a short time plays an important part.Modem turbulence models must possess universality, invariance under transformations of the coordinate system, adaptability to numerical methods, and simplicity. At present, there is no model that satisfies all these requirements.In this study the development of a universal one-equation model for the turbulent viscosity v t is continued. The first variant of this model was proposed by Kovasznay [1]. Subsequently, in [2--6] the model was modified and improved. One of the modifications of the model "vt-90" was involved in the "collaborative testing of turbulence models-1990/91" organized by Stanford University [7]. Almost half the hundred participants in this testing program used modifications of the well-known "k--e model" [8]. Many participants used models containing equations for all the components of the Reynolds stress tensor. The inauspicious result of this international effort is the conclusion that none of the models, including the complex multi-equation models, describes the entire spectrum of flows chosen by the organizers (P. Bradshaw, B. Launder, and J. Lumley) for model testing purposes.In this connection, it is desirable to employ the models which are simplest and most economical as regards machine time. The authors of [9], in which a new interesting variant of the turbulent viscosity model is proposed, came to the same conclusion. Discussion of the models with one of the authors of that study --Professor P. Spalart --led to intensification of the work on the new improved variant "vt-92" described below. In addition, a methodology reflecting the views of the authors on how to obtain a quantitative estimate of the accuracy and universality with which a particular model describes real flows is presented. PRELIMINARY REMARKSThe "collaborative testing of turbulence models-1990/91" [7] This model is distinguished by the attempt to take into account the effects associated with the axisymmetry of the flow. For this purpose a correction function, which depends on the parameter r2r 1/vt, where r is determined in accordance with the following rules, is introduced. In the neighborhood of the point x o we introduce a surface A: ~t(x) =const=vt(Xo). We construct a plane B comaining the vectors grad(vt) and curl U. We define r as the radius of curvature of t...