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Nonlinear stability of nonstationary cross-flow vortices in compressible boundary layers. (English) Zbl 0872.76040

This paper is concerned with the nonlinear evolution of nonstationary cross-flow vortices in a compressible three-dimensional boundary layer. Unsteady nonlinear critical-layer theory is used to extend previous work of J. S. B. Gajjar [IMA J. Appl. Math. 53, No. 3, 221-248 (1994; Zbl 0818.76029)] to flows with two critical layers. For the limit of large Reynolds numbers and low-frequency cross-flow vortices that have small growth rates, the nonlinear evolution equations are derived but not solved. Nevertheless, for special cases like the linear theory, analytic expressions are obtained which demonstrate the effects of parameters on the stability properties.

MSC:

76E30 Nonlinear effects in hydrodynamic stability
76N20 Boundary-layer theory for compressible fluids and gas dynamics

Citations:

Zbl 0818.76029
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References:

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