Stability of three-dimensional boundary layers
Stability of three-dimensional boundary layers
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DOI：
10.2514/3.50773
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发表时间：
1979
期刊：
影响因子：
2.5
通讯作者：
A. Nayfeh
中科院分区：
文献类型：
--
作者：
A. Nayfeh
发展了三维增长边界层的线性稳定性理论。用多尺度法建立了描述扰动的复振幅和波数的时空演化的偏微分方程组。一般而言，除非满足某些条件，否则这些方程是椭圆型的。对于单色扰动，这些条件要求复群速度的分量之比为实数，从而将扰动的增长方向与扰动波角联系起来。对于不增长的边界层，此条件退化为实数da/d/3，其中a和&是流向和横向的复波数，与鞍点法得到的结果一致。对于波包，这些条件要求复群速度的分量是实数。在所有情况下，演化方程都归结为沿着实群速度方向的非齐次常微分方程组。
A theory is developed for the linear stability of three-dimensi onal 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 elliptic, unless certain conditions are satisfied. For a monochromatic disturbance, these conditions demand that the ratio of the components 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 da/d/3 being real, where a and & 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 ordinarydifferential equations along real group velocity directions.