Incompressible boundary layer with counterflows at a given pressure gradient

Two-dimensional laminar flow of a viscous incompressible fluid near a flat surface is considered at high Reynolds numbers. The influence exerted on the Blasius boundary layer by a body moving downstream with a low velocity relative to the plate is studied within the framework of asymptotic theory. A special case is investigated in which an external small body modeled by a potential dipole moves downstream at a constant velocity. Formally, this problem is nonstationary on a stationary plate, but, after passing to a coordinate system comoving with the dipole, it is described by stationary viscous sublayer equations, but on the wall moving upstream. An original method for solving such problems with counterflows is proposed. Specifically, near the surface, an upstream flowing fluid layer is chosen, above which the fluid in the boundary layer flows downstream. An exact analytical solution of the linear problem is found for a potential dipole of low intensity, and a numerical solution of the nonlinear problem is determined at high dipole intensities. Even in the linear approximation, the solutions involve closed and open separation regions near the line of zero streamwise velocity. The found solutions can be used to refine measurement techniques for boundary-layer flow characteristics measured with hotwire anemometers, pressure meters, and other sensors mounted on a moving coordinate input device within a boundary layer developing on solid and perforated wind tunnel walls.