ON THE NEUTRAL STABILITY OF SPANWISE-PERIODIC BOUNDARY-LAYER AND TRIPLE-DECK FLOWS

SUMMARY The neutral stability of spanwise-periodic mean flows to three-dimensional Tollmien- Schlichting (TS) disturbances is considered theoretically and numerically. The flows under consideration are (i) a triple-deck flow with a simple pressure-displacement law and (ii) a boundary layer flow on the point of separation. In both cases the stability problem is formulated and a necessary condition for the existence of neutral solutions is derived. Using a numerical approach we show that this condition is not met in case (i) for any periodic spanwise dependence and in case (ii) provided spanwise variations in the mean flow are sufficiently small. This means that neutral waves are not rendered possible by a three-dimensional skin friction in case (i) and are unlikely to exist in case (ii) for physically realistic mean flows. The implications of these results with regard to the possibility of the occurrence of vortex-TS interactions in such flows is discussed.