Linear stability theory predicts two or more types of unstable disturbances in a sufficiently high-speed boundary layer. These include the first mode, which is similar to the Tollmien-Schlichting waves found in low-speed flows, and the second mode, which does not depend strongly on the viscosity. Generally, the most unstable first mode is three dimensional while the most unstable second mode is two dimensional. The interaction between these two spatially unstable modes are studied by direct solution of the three-dimensional Navier-Stokes equations. It is found that the two-dimensional second mode causes a significant increase in the nonlinearity and in the three-dimensionality of the flow field. The results suggest that this interaction may accelerate transition for flows where the second mode has a significant growth rate.
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