On nonlinear TollmienSchlichting/vortex interaction in threedimensional boundary layers
Abstract
The instability of an incompressible threedimensional boundary layer (that is, one with crossflow) is considered theoretically and computationally in the context of vortex/wave interactions. Specifically the work centers on two low amplitude, lowerbranch TollmienSchlichting waves which mutually interact to induce a weak longitudinal vortex flow; the vortex motion, in turn, gives rise to significant wavemodulation via wallshear forcing. The characteristic Reynolds number is taken as a large parameter and, as a consequence, the waves' and the vortex motion are governed primarily by tripledeck theory. The nonlinear interaction is captured by a viscous partialdifferential system for the vortex coupled with a pair of amplitude equations for each wave pressure. Three distinct possibilities were found to emerge for the nonlinear behavior of the flow solution downstream  an algebraic finitedistance singularity, far downstream saturation or fardownstream wavedecay (leaving pure vortex flow)  depending on the input conditions, the wave angles, and the size of the crossflow.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 May 1993
 Bibcode:
 1993STIN...9411377D
 Keywords:

 Cross Flow;
 Incompressible Boundary Layer;
 Three Dimensional Boundary Layer;
 TollmienSchlichting Waves;
 Vortices;
 Wave Interaction;
 Boundary Layer Flow;
 Nonlinear Systems;
 Reynolds Number;
 Fluid Mechanics and Heat Transfer