Жазық пластинадағы Блазиус шекаралық қабаты

Two dimensional laminar boundary layer that forms on a semi infinite plate
In physics and fluid mechanics, a Blasius boundary layer (named after Paul Richard Heinrich Blasius) describes the steady two dimensional laminar boundary layer that forms on a semi infinite plate which is held parallel to a constant unidirectional flow. Falkner and Skan later generalized Blasius' solution to wedge flow (Falkner–Skan boundary layer), i. e. flows in which the plate is not parallel to the flow.

The Blasius solution is not unique from a mathematical perspective, as Ludwig Prandtl himself noted it in his transposition theorem and analyzed by series of researchers such as Keith Stewartson, Paul A. Libby. To this solution, any one of the infinite discrete set of eigenfunctions can be added, each of which satisfies the linearly perturbed equation with homogeneous conditions and exponential decay at infinity. The first of these eigenfunctions turns out to be the derivative of the first order Blasius solution, which represents the uncertainty in the effective location of the origin.

Since the convection due to suction and the diffusion due to the solid wall are acting in the opposite direction, the profile will reach steady solution at large distance, unlike the Blasius profile where boundary layer grows indefinitely. The solution was first obtained by Griffith and F. W. Meredith. For distances from the leading edge of the plate , both the boundary layer thickness and the solution are independent of given by

Stewartson studied matching of full solution to the asymptotic suction profile.

Since the boundary layer equations are Parabolic partial differential equation, the natural coordinates for the problem is parabolic coordinates. The transformation from Cartesian coordinates to parabolic coordinates is given by