= Boundary-layer transition
\b[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.<Laminar-Boundary-Layer Oscillations and Transition on a Flat Plate by G. B. Schubauer and H. K. Skramstad>[NACA-TR-909, repository abstract: damping screens, low stream turbulence and observed laminar-layer oscillations]{ref}
The local <Reynolds number>
$$
\operatorname{Re}_x=\frac{Ux}{\nu}
$$
compares inertia with viscosity using external speed $U$, distance $x$ from the leading edge and <kinematic viscosity> $\nu$. For stipulated $U=10\,\mathrm{m\,s^{-1}}$, $x=0.50\,\mathrm m$ and $\nu=1.5\times10^{-5}\,\mathrm{m^2\,s^{-1}}$, it is approximately $3.33\times10^5$. 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 obeys
$$
\frac{dA}{dx}=\sigma(x)A,\qquad
\frac{A(x)}{A(x_0)}=\exp\!\left(\int_{x_0}^{x}\sigma(s)\,ds\right).
$$
If a stipulated breakdown amplitude is 100 times the initial amplitude, the integrated growth needed is $\ln100\approx4.61$. Increasing the initial amplitude tenfold reduces that requirement to $\ln10\approx2.30$. 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.
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