Is the ambient transverse velocity in a boundary layer flow non-zero or zero?

Abstract

The concept of boundary layer flow, introduced in 1904 by Prandtl, is a popular field in Fluid Mechanics for engineers, physicists and mathematicians. In the classical Blasius boundary layer flow the transverse (normal) velocity reaches a finite value and remains constant in the free stream. If this finite vertical speed will be added to the free stream speed the resulting velocity in the free stream will be greater than the original velocity upstream of the plate which is irrational. This phenomenon has been marked and discussed in many Fluid Mechanics textbooks without a satisfactory explanation. In the present work we present a definite explanation by solving the complete Navier-Stokes equations. It is found that the real ambient transverse velocity is zero and not finite as it is predicted by the boundary layer theory. The same is valid in the classical free convection flow along a vertical isothermal plate.