Boundary Layer Thickness
Air slides over a flat plate and a thin slowed sheet forms along it. Drag the speed slider and watch that sheet thin out as the flow turns from smooth to turbulent.
Air slides over a flat plate and a thin slowed sheet forms along it. Drag the speed slider and watch that sheet thin out as the flow turns from smooth to turbulent.
When fluid flows over a solid surface, friction holds the layer nearest the wall nearly still. That slowed sheet is the boundary layer. Its speed climbs from zero at the wall to the free-stream speed at its outer edge.
This simulator lays a flat plate in a steady air stream. The layer begins at the leading edge, grows downstream, and can change character partway along.
The boundary layer decides drag, heat transfer and whether flow separates from a surface. Its thickness is small, but it sets much of the behaviour engineers care about.
Two ideas matter most: the layer is laminar until the local Reynolds number crosses a critical value, and after transition it thickens far more quickly than it did while laminar.
Far above the plate the air is undisturbed and moves at the free-stream speed U∞ you set. That speed, together with distance along the plate, drives everything that follows.
Local Reynolds number equals speed times distance divided by viscosity. It is small at the leading edge and rises steadily downstream, tracking how far the layer has had time to develop.
While the Reynolds number stays below about 500,000 the layer is smooth and ordered, and is called laminar. Beyond that critical value the flow becomes turbulent, and the transition point marks the change.
Turbulence mixes the flow far more vigorously than smooth laminar motion. Downstream of transition the layer grows more steeply, and its velocity profile becomes fuller, with a sharp rise close to the wall.
The marker at the end of the plate reads off the local thickness δ(x). Raising the free-stream speed lifts the Reynolds number, moves the transition point upstream and leaves a thinner layer at the exit.
It is the thin sheet of fluid next to a surface where friction slows the flow down. At the wall the speed is zero, and it climbs back to the free-stream value at the outer edge of the layer.
Friction acts over a longer stretch of plate as the flow travels further, so more fluid is slowed and the layer grows. On a laminar stretch it grows as the square root of distance.
It is the place where the local Reynolds number passes about 500,000 and the layer changes from smooth laminar flow to turbulent flow. Downstream of it the layer thickens much faster.
A higher speed raises the Reynolds number at every station, which pushes the transition point upstream and makes the layer thinner for the same plate length.
Each curve plots speed against height at one station. A laminar profile is a gentle parabola; a turbulent profile is fuller, with a steeper rise close to the wall.
No. Boundary layers are very thin compared with the plate length, so the vertical direction is exaggerated about fifteen times in the drawing to make the shape visible.