Mathematical Physics

   

Dynamics of Boundary Layer Separating from Surface to the Outer Flow

Authors: Sergey V. Ershkov

Solving the Navier-Stokes equations for 3D boundary layer of the incompressible flow of Newtonian fluids is the most unsolved problem in fluid mechanics. A lot of authors have been executing their researches to obtain the analytical and semi-analytic solutions for the boundary layer approximation of Navier-Stokes equations, even for example for 2D case of compressible gas flow. But there is an essential deficiency of 3D solutions for the boundary layer indeed. In current research, an elegant ansatz is developed to obtain 3D solutions for the boundary layer approximation of Navier-Stokes equations of incompressible fluids (in the vicinity of the point of separating of boundary layer from surface to the outer ideal flow). The governing equation for such the process is proved to be the Poisson equation for each the component of velocity field of boundary layer flow, which could nevertheless be reduced to the Laplace equation in case of the uniform outer flow.

Comments: 10 pages, 7 figures; Keywords: Navier-Stokes equations, non-stationary flow, boundary layer

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Submission history

[v1] 2018-05-08 08:04:23

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