In a laminar boundary layer, if the initial disturbance spectrum is nearly infinitesimal and random (with no discrete frequency peaks), the initial instability will occur as two-dimensional Tollmien–Schlichting waves, travelling in the mean flow direction if compressibility is not important. However, three-dimensionality soon appears as the Tollmien–Schlichting waves rather quickly begin to show variations.
There are known to be many paths from Tollmien–Schlichting waves to turbulence, and many of them are explained by the non-linear theories of flow instability.