On the modulational instability of O(1) amplitude waves in supersonic boundary layers

Document Type

Article

Publication Date

1-1-1997

Abstract

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.

Identifier

0031213190 (Scopus)

Publication Title

SIAM Journal on Applied Mathematics

External Full Text Location

https://doi.org/10.1137/s0036139995285765

ISSN

00361399

First Page

929

Last Page

958

Issue

4

Volume

57

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