INFLUENCE OF CROSS-FLOW ON NONLINEAR TOLLMIEN-SCHLICHTING VORTEX INTERACTION

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.