Abstract
On the basis of Stokes separated flows, examples of separated flows described by the Navier-Stokes equations of a viscous incompressible fluid are constructed. These flows are represented by series convergent in a certain non-zero neighborhood of a flat contour immersed in the flow. In this neighborhood, the series have the same structure as those for the basic Stokes flows. Examples of the regions in which the series segments chosen give only a slight deviation from the numerical solutions of the Navier-Stokes equations are presented. The comparison between inviscid separated flows (without the no-slip condition on the contour) and viscous flows of the same structure (with the no-slip condition) shows that the viscosity does not play a decisive role in the formation of separation or the type of streamline approach to or departure from the contour.
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REFERENCES
Yu. D. Shmyglevskii and A.V. Shcheprov, “On vortex systems in a viscous fluid near a boundary corner point,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 1, 62 (2002).
B.V. Pal'tsev and Yu. D. Shmyglevskii, “On the approach of a separating streamline to a contour in a plane-parallel viscous-fluid flow,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 2, 76–89 (2002).
J.W. Strutt (Baron Rayleigh), “Steady motion in a corner of a viscous fluid,” in: Hydrodynamic Notes. 351. Scientific Papers. V.6, Univ. Press., Cambridge (1920), pp. 18–21.
I. G. Petrovskii, Lectures on Partial Differential Equations [in Russian], Fizmatgiz, Moscow (1961).
A. A. Samarskii and A.V. Gulin, Numerical Methods [in Russian], Nauka, Moscow (1989).
Yu. D. Shmyglevskii, Analytical Studies in Fluid Dynamics [in Russian], Editorial URSS, Moscow (1999).
W.R. Dean and P.E. Montagnon, “On the steady motion of viscous liquid in a corner,” Proc. Cambr. Phil. Soc., 45, Pt. 3, 389–394 (1949).
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Shmyglevskii, Y.D., Shcheprov, A. On Plane-Parallel Separated Flows of an Incompressible Fluid near Flat Boundaries. Fluid Dynamics 37, 674–683 (2002). https://doi.org/10.1023/A:1021308016522
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DOI: https://doi.org/10.1023/A:1021308016522