Introduction to Fluid Mechanics

Boundary Layers

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The Reynolds number of a flow is the ratio of intertial forces to viscous forces. This can be derived from a scaling argument. In a boundary layer, the characteristic lengthscale is the distance from the start of the boundary layer.

By considering a large control volume, we can obtain an expression for the momentum loss by the fluid in a boundary layer in terms of the shear stress at the boundary. This is valid for both laminar and turbulent boundary layers.

As the Reynolds number in a boundary layer increases (i.e. further from the start of the boundary layer), the ratio between the inertial and viscous forces increases. Small perturbations become unstable and grow into vortices and eventually turbulence. This increases the rate of momentum transfer in the boundary layer and therefore the rate of the boundary layer's growth.

When a boundary layer becomes turbulent, streamwise momentum from the free stream diffuses towards the surface more quickly. If the boundary layer is in an adverse pressure gradient then this extra momentum diffusion allows the boundary layer to withstand a larger pressure gradient before it separates. This is often beneficial.

Boundary layer separation and boundary layer transition to turbulence are entirely separate phenomena. They can both be caused by an adverse pressure gradient, however, and this leads some students to confuse the two. This clip explains how they both arise and how they differ.

If a laminar boundary layer separates and then becomes turbulent, the increased momentum transfer can cause the boundary layer to re-attach.

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