The generation of Tollmien-Schlichting waves by long wavelength free stream disturbances

The paper is primarily concerned with explaining how very long wavelength free stream disturbances are able to generate very short wavelength Tollmien-Schlichting waves in laminar boundary layers. Consideration is given to the case where the disturbances are of small amplitude and have harmonic time dependence and where the Mach number is effectively zero. It is shown that the free stream wavelength reduction occurs as a result of nonparallel flow effects which can arise from: (1) the slow viscous growth of the boundary layer, and (2) small but abrupt changes in surface geometry that produce only very weak static pressure variations. Analyses of these two mechanisms are carried out by linearizing the unsteady motion about an appropriate steady flow and asymptotically expanding the result in inverse powers of an appropriate Reynolds number. The analyses are compared with each other and with available experimental data, and they are used to explain the physics of the two mechanisms.