Flow Over a Surface Builds a Thin Boundary Layer
Even a fast river is nearly still just above its bed. To see the thin layer clinging to a surface — where the speed climbs from zero up to the free stream — drag the free-stream speed of the flow over a flat plate.
Flow moving uniformly over a flat plate slows to zero near the wall because of no-slip. Far away it keeps the free-stream speed U∞, but near the wall the arrows shorten and bend down to zero. This thin band where the speed changes from 0 to U∞ is the boundary layer, and its thickness is called δ. Drag the free-stream speed U∞ and the outer arrows scale as a whole, yet at the wall it is always zero.
The boundary layer starts at the leading edge and thickens downstream, because the wall drags more and more layers into slowing down. Drag the measuring position x and the boundary-layer edge swells like √x. It is razor-thin at the front and thickens, ever more slowly, as you go.
A boundary layer also starts laminar and switches to turbulent at some point. Toggle to compare. The laminar layer is thin and smooth and grows slowly, while the turbulent layer mixes vigorously, is thicker, and has a fuller profile packed up near the wall. The switch happens once the critical Rex is passed.
Zoom in right next to the wall. The speed is zero at the wall, but the slope du/dy rising up from that zero sets the friction the wall feels — the wall shear stress (skin friction) τw = μ (du/dy)|wall. Drag the free-stream U∞ and the near-wall slope steepens and τw grows. Summed up, this skin friction becomes one part of the drag on a body.
The thickness of a laminar boundary layer follows a clean formula: δx = 5√Rex, that is δ ≈ 5x√Rex. The larger the local Reynolds number Rex = U∞ xν, the (relatively) thinner the layer. Drag Rex and δx shrinks as 1√Rex. So a faster, larger flow keeps a thinner layer on the surface, and the design of airplane wings, golf balls, and ship hulls all rests on this. In the next lesson we follow how this boundary layer separates and creates drag.