Tollmien–Schlichting wave

In fluid dynamics, a Tollmien–Schlichting wave (often abbreviated T-S wave) is a streamwise instability which arises in a viscous boundary layer. It is one of the more common methods by which a laminar boundary layer transitions to turbulence. The waves are initiated when some disturbance (sound, for example) interacts with leading edge roughness in a process known as receptivity. These waves are slowly amplified as they move downstream until they may eventually grow large enough that nonlinearities take over and the flow transitions to turbulence.

These waves, originally discovered by Ludwig Prandtl, were further studied by two of his former students, Walter Tollmien and Hermann Schlichting for whom the phenomenon is named.

In order for a boundary layer to be absolutely unstable (have an inviscid instability), it must satisfy Rayleigh's criterion; namely ${\displaystyle D^{2}U=0}$ where ${\displaystyle D}$ represents the y-derivative and ${\displaystyle U}$ is the free stream velocity profile. In other words, the velocity profile must have an inflection point to be unstable.

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