Tollmien-Schlichting waves

In fluid dynamics, a Tollmien–Schlichting wave (often abbreviated T-S wave) is a streamwise unstable wave which arises in a bounded shear flow (such as boundary layer and channel flow). It is one of the more common methods by which a laminar bounded shear flow 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 after whom the phenomenon is named.

Also, T-S wave is defined as the most unstable eigen-mode of Orr-Sommerfeld equations (Page 64).

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.

...
Wikipedia