Abstract:

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.

Key words: parabolized stability equation, characteristic, sub-characteristic, compressible flow, boundary layer