 Boundary-layer transition

Boundary-layer transition is the development of turbulent flow from an initially laminar flow within a boundary layer. A laminar boundary layer can contain small, organized disturbances before the fluctuations become turbulent. Thus detecting an oscillation is evidence of a disturbance, not by itself proof that transition is complete.

A motivating experiment by G. B. Schubauer and H. K. Skramstad studied a flat plate while reducing the surrounding stream's turbulence intensity with damping screens. At unusually low stream disturbances, they observed oscillations in the laminar boundary layer. Controlling the external disturbances made internal disturbance development experimentally distinguishable.^[ref]

The local Reynolds numbercompares inertia with viscosity using external speed $U$, distance $x$ from the leading edge and kinematic viscosity $\nu$. For stipulated $U=10\mathrm{m}{\mathrm{s}}^{-1}$, $x=0.50\mathrm{m}$ and $\nu =1.5\times 10^{-5}{\mathrm{m}}^2{\mathrm{s}}^{-1}$, it is approximately $3.33\times 10^5$. This calculation specifies a flow scale; it is not a universal transition criterion. Surface condition, surrounding disturbances and the pressure gradient also matter.

A simple model of boundary-layer disturbance amplification makes this sensitivity explicit. Suppose a small disturbance amplitude obeysIf a stipulated breakdown amplitude is 100 times the initial amplitude, the integrated growth needed is $\ln 100\approx 4.61$. Increasing the initial amplitude tenfold reduces that requirement to $\ln 10\approx 2.30$. This is an illustrative linear growth model, not a calibrated predictor of turbulent breakdown. It explains why specifying Reynolds number without specifying the disturbance environment can leave the observed transition location undetermined.