Qualitative Features of Boundary Layer Separation

Here X is the curvilinear coordinate along the surface of the body and Y is the coordinate normal to the surface. 

The boundary layer equations are valid only in the region between the front stagnation point and the separation point. Behind the separation point there is a wake region with absolutely different hydrodynamic laws. The position of the separation point can be determined either experimentally or by using numerical or approximate analytical methods. 

As Re increases, the adjacent vortices are elongated and shedding of vortices occurs (Karman s vortices are formed). Finally, for Re 1000, the remote wake becomes completely turbulent [117]. At the same time, the separation point moves toward the midsection and even a bit farther upstream. For such values of Re, we can speak about a pronounced boundary layer. In a large part of the boundary layer, the flow remains laminar [486], Strong turbulence within the boundary layer occurs for considerably higher Reynolds numbers (Re 2x 105), at which the cylinder drag drops rapidly [117], This phenomenon is called the drag crisis. 

In what follows we consider the laminar boundary layer in a cross flow past a circular cylinder. This problem is also of practical importance, since tube elements are widely used in industrial equipment. 

Cross flow past a cylinder. The problem on a cross flow past a cylinder comprises Eqs. (1.8.1) and boundary conditions (1.8.2)—(1.8.3). For a circular cylinder, we have [427] 

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