The necessity of correcting differential semiempirical turbulence models to calculate circulating fl ows of an incompressible viscous fl uid is discussed. Approaches to taking account of the infl uence of the curvature of streamlines on turbulence characteristics arereviewed. Experience gained in modeling numerically twodimensional separated fl ows in a square and a cylindrical cavity on the wall of a plane-parallel channel is analyzed; an additional semiempirical constant in the expression for vortex viscosity of a modifi ed shear-stress-transfer model is substantiated.Introduction. The signifi cant difference in results of numerical modeling of circulating fl ow in the circular cavity on the wall of a rotating channel [1] from the corresponding data obtained with the Doppler laser velocimeter on the experimental setup in Southampton [2] increasingly draws attention to the idea of correction of semiempirical turbulence models used to close Reynolds-averaged Navier-Stokes equations [3] with account of the infl uence of the streamline curvature.In this connection, the present work seeks to analyze experience gained in modeling numerically separated fl ows with turbulence models, in particular, with the frequently used semiempirical turbulence model, i.e., the Mentershear-stresstransfer k-ω model (MSST) in the versions of the year 1993 (MSST1993) and of the year 2003 (MSST2003) [4, 5]. Also, the present work seeks to substantiate the semiempirical constant in the expression for vortex viscosity in the MSST 2003 version [5] using, as examples, the calculations of experimental analogs of separated fl ows of an incompressible viscous medium in a square and a cylindrical cavity on the wall of a plane-parallel channel.Historical Review of Investigations into the Correction of Semiempirical Turbulence Models with Account of the Infl uence of the Streamline Curvature. It is common knowledge that semiempirical models of closure of Reynoldsaveraged Navier-Stokes equations [3, 6] have been constructed for calculation of wall fl ows. In any event, calibration of the constants for them is based on measurements that have been performed on special test beds for model fl ows [7]. Turbulence models are not universal. Thus, the turbulent Prandtl number for the boundary layer is equal to 0.9, and for the jet fl ow, to 0.6 [8]. At the same time, in intricate wall fl ow, one cannot, in practice, single out jet fl ows and, in modeling them using package technologies, takes the turbulent Prandtl number as constant and equal to 0.9 [9]. Also, it should be noted that algebraic turbulent models for calculation of fl ows in curvilinear channels include curvature corrections in expressions for a turbulence scale [3]. Rotation corrections seem even more signifi cant as far as their infl uence, primarily, on velocity profi les is concerned [10].

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