二维抛物化稳定性方程的特征分析

在对抛物化稳定性方程(PSE)的基本流场没有做任何近似假定的情况下，分析了PSE的特征性质。分析表明，当法向速度不为零时，PSE有一个非零主特征值，其余主特征值都为零。PSE的次特征值与扰动波的空间波数α有关，α的实部代表扰动波的波动情况，它可以直接导致复特征值出现；α的虚部表示扰动波的增长(衰减)情况，当它的绝对值超过一定范围时，也会在边界层内亚声速区的局部区域导致复特征值出现。增大求解PSE的空间推进步长，可以克服PSE的椭圆性。

Characteristics Analysis of Two-dimensional Parabolized Stability Equations

The characteristics of parabolized stability equations (PSE) are analyzed without any approximate hypothesis of base flows. The analysis indictes that there is a nonzero main characteristic due to the nonzero transverse velocity, and all the other main characteristics of PSE are zero. The sub-characteristics are related to the spacial wave number (α) of a disturbance. The real part of α denotes the wavelength of the disturbance, and a nonzero real part of α leads to complex sub-characteristics. The image part of α denotes the increase/decrease rate of the disturbance, and a nonzero image part of α would lead to complex sub-characteristics if the absolute value of the image part is large enough. The ellipticity of PSE tends to be alleviated by a large matching step size.