A theory is developed for the linear stability of three-dimensional growing boundary layers. The method of multiple scales is used to derive partial-differential equations describing the temporal and spatial evolution of the complex amplitudes and wavenumbers of the disturbances. In general, these equations are eliptic, unless certain conditions are satisfied. For a monochromatic disturbance, these conditions demand that the ratio of the component of the complex group velocity be real, thereby relating the direction of growth of the disturbance to the disturbance wave angle. For a nongrowing boundary layer, this condition reduces to d alpha/d beta being real, where alpha and beta are the complex wavenumbers in the streamwise and crosswise directions, in agreement with the result obtained by using the saddle-point method. For a wavepacket, these conditions demand that the components of the complex group velocity be real. In all cases, the evolution equations are reduced to inhomogeneous ordinary-differential equations along real group velocity directions. (DePo)
Stability of three-dimensional boundary layers
Stabilitaet dreidimensionaler Grenzschichten
AIAA Journal ; 18 , 4 ; 406-416
1980
11 Seiten, 35 Quellen
Article (Journal)
English
Stability of Three-Dimensional Boundary Layers
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