Ag. Walton et Ra. Patel, ON THE NEUTRAL STABILITY OF SPANWISE-PERIODIC BOUNDARY-LAYER AND TRIPLE-DECK FLOWS, Quarterly Journal of Mechanics and Applied Mathematics, 51, 1998, pp. 311-328
The neutral stability of spanwise-periodic mean flows to three-dimensi
onal Tollmien-Schlichting (TS) disturbances is considered theoreticall
y and numerically. The flows under consideration are (i) a triple-deck
flow with a simple pressure-displacement law and (ii) a boundary laye
r 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 con
dition is not met in case (i) for any periodic spanwise dependence and
in case (ii) provided spanwise variations in the mean flow are suffic
iently small. This means that neutral waves are not rendered possible
by a three-dimensional skin friction in case (i) and are unlikely to e
xist in case (ii) for physically realistic mean flows. The implication
s of these results with regard to the possibility of the occurrence of
vortex-TS interactions in such flows is discussed.