On the modulational instability of large amplitude waves in supersonic boundary layers
摘要：
The evolution of O(1) amplitude Tollmien-Schlichting waves in a supersonic boundary layer is investigated. Disturbances whose wavenumber and frequency vary slowly in time and space are described using a phase equation type of approach. Unlike in the incompressible case, we find that the initial bifurcation to a finite amplitude Tollmien-Schlichting wave is subcritical for most Mach numbers. In fact the bifurcation is supercritical only for a small range of Mach numbers and even then for only a finite range of wave propagation angles. The modulational instability of large amplitude wavetrains is considered and is shown to be governed by an equation similar to Burgers equation but with the viscous term replaced by a fractional derivative. A numerical investigation of the solution of this equation is described. It is shown that uniform wavetrains are unstable.
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DOI：
10.1137/S0036139995285765
被引量：
年份：
1997
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