Abstract
Three-dimensional growth of Tollmien-Schlichting (T-S) waves excited at two frequencies are examined both experimentally and numerically in plane Poiseuille flow. The two T-S waves excited have nearly the same in amplitude and their frequencies (or wave numbers) are close to each other. So, the associated velocity fluctuations are highly modulated in amplitude not unlike T-S waves observed in natural transition. It is found that the three-dimensional (Klebanoff-type) wave growth occurs locally when the maximum amplitude of the linear combination of two T-S waves exceeds 1.0–1.2% of the center-plane velocity in terms of u-fluctuation, this being almost the same as the threshold found for a purely sinusoidal T-S wave. It should be emphasized that when such a local threshold condition is satisfied, the three-dimensional waves are amplified in succession around the maximum-amplitude phase of the modulated two-dimensional waves.
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