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Influence of Streamwise Vortices on Tollmien-Schlichting Waves
An analysis is presented of the influence of steady quasiperiodic streamwise vortices on Tollmien-Schlichting (TS) waves. The vortices act as parametric exciters for the TS waves. The present analysis is for the subharmonic resonance in which the spanwise wavenumber of the vortices is twice that of the TS wave. Floquet theory is used to derive an eigenvalue problem for the complex streamwise wavenumber, which is then solved using a shooting technique. The results show that there are two components of the solution, one is stabilized and the other is destabilized by the vortices. For the same flow characteristics, calculations were obtained from the theory which Nayfeh [J. Fluid Mech. 1 0 7, 441 (1981)] developed using the method of multiple scales. The results obtained from both approaches are in excellent agreement.