Dar. Davis et Ft. Smith, INFLUENCE OF CROSS-FLOW ON NONLINEAR TOLLMIEN-SCHLICHTING VORTEX INTERACTION, Proceedings - Royal Society. Mathematical and physical sciences, 446(1927), 1994, pp. 319-340
The transition of an incompressible three-dimensional boundary layer w
ith strong cross-flow is considered theoretically and computationally
in the context of vortex/wave interactions. Specifically the work cent
res on two lower-branch Tollmien-Schlichting waves which mutually inte
ract nonlinearly to induce a longitudinal vortex flow. The vortex moti
on in turn gives rise to significant wave modulation via wall-shear fo
rcing. The characteristic Reynolds number is large and, as a consequen
ce, the waves' and the vortex motion are governed primarily by triple-
deck theory. The nonlinear interaction is captured by a viscous partia
l-differential system for the vortex coupled with a pair of amplitude
equations for each wave pressure. Following analysis and computation o
ver a wide range of parameters, three distinct responses are found to
emerge in the nonlinear behaviour of the flow solution downstream: an
algebraic finite-distance singularity, far-downstream saturation or fa
r-downstream wave decay leaving pure vortex flow. These depend on the
input conditions, the wave angles and the size of the cross flow.