The concept of** boundary layers** is important in all viscous fluid dynamics, aerodynamics, and heat transfer theory. Basic characteristics of all laminar and turbulent boundary layers are shown in the developing flow over a flat plate. The stages of the formation of the boundary layer are shown in the figure below:

**Boundary layers** may be either** laminar** or **turbulent,** depending on the value of **the Reynolds number**. Also, here the Reynolds number represents the ratio of inertia forces to viscous forces and is a convenient parameter for predicting if a flow condition will be laminar or turbulent. It is defined as:

in which V is the mean flow velocity, D is a characteristic linear dimension, ρ fluid density, μ dynamic viscosity, and ν kinematic viscosity.

The boundary layer is laminar for** lower Reynolds numbers**, and the streamwise velocity uniformly changes as one moves away from the wall, as shown on the left side of the figure. **As the Reynolds number increases** (with x), the** flow becomes unstable**. Finally, the boundary layer is turbulent for higher Reynolds numbers, and the streamwise velocity is characterized by unsteady (changing with time) swirling flows inside the boundary layer.

**The transition from laminar to turbulent** boundary layer occurs when Reynolds number at x exceeds **Re _{x} ~ 500,000**. The transition may occur earlier, but it is dependent especially on the

**surface roughness**. The turbulent boundary layer thickens more rapidly than the laminar boundary layer due to increased shear stress at the body surface.

See also: Boundary layer thickness.

See also: Tube in crossflow – external flow.

**Special reference:** Schlichting Herrmann, Gersten Klaus. Boundary-Layer Theory, Springer-Verlag Berlin Heidelberg, 2000, ISBN: 978-3-540-66270-9