Turbulent Boundary Layer
Turbulent boundary layers are very different from laminar ones,
the turbulent boundary layer is characterized by chaotic and irregular velocity fluctuations,
and there is almost no general law for the velocity profile.
Moreover, the outer edge of the boundary layer does not remain steady,
so the boundary layer thickness at the same streamwise position may vary significantly with time
The alternation of turbulent and laminar flows is called the intermittent motion of the turbulent boundary layer,
and the intermittent factor can be defined according to the proportion of time occupied by turbulent and laminar flows
As the fluid flows over a long flat plate, the boundary layer will always be laminar at the entrance region, and change from laminar to turbulent (known as laminar-to-turbulent transition) at a critical distance where the flow cannot remain stable
The turbulent boundary layer flow is strongly unsteady. Although the average velocity profile is quite regular, the velocity fluctuations still have an important influence on the averaged flow. Subsequently, the averaged turbulent boundary layer equation is different from the laminar one, with the terms of fluctuating quantities in the equation.
1Hongwei Wang (2023). A Guide to Fluid Mechanics. National Defense Industry Press.