Abstract
The growth of Tollmien-Schlichting (T-S) waves in a Blasius boundary layer is studied using high-Reynolds-number asymptotic methods. Attention is focused on weakly nonlinear resonant-triad interactions. Most previous work has concentrated on the interaction of a two-dimensional wave with a pair of oblique subharmonics. Here, we consider non-aligned triads in which all three modes may be oblique. Moreover, we allow the waves to be weakly modulated in time and in the streamwise and spanwise directions, so that localised wave-packets can be described. Analytic and numerical solutions of the governing amplitude equations indicate that the two most oblique modes may grow super-exponentially for a time, as a result of quadratic interaction with the third mode, in both the aligned and non-aligned cases. Subsequently, however, cubic (‘wave-vortex’) interactions may become significant, and this stage of development may be quite different in the two cases.
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