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

TL;DR

This paper investigates whether the ambient transverse velocity in boundary layer flows is truly non-zero, providing a definitive explanation through solving Navier-Stokes equations, and concludes that it is actually zero, contrary to classical assumptions.

Contribution

The paper offers a rigorous solution to Navier-Stokes equations demonstrating that the ambient transverse velocity in boundary layers is zero, challenging traditional boundary layer theory assumptions.

Findings

Ambient transverse velocity is zero in boundary layers.

Classical boundary layer theory predicts a finite transverse velocity, which is shown to be incorrect.

The result applies to both boundary layer flow and free convection along a vertical plate.

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.