STUDY ON DOMINANT EIGENSPECTRUM MODES OF LIFT-UP AND ORR TRANSIENT MECHANISMS

Transient growth is one of the crucial physical mechanisms of boundary layer transition, typically dominated by the lift-up and Orr mechanisms. To clarify the correlation between these two mechanisms and eigenspectrum modes, linear stability and transient growth analyses are performed on compressible flat-plate Blasius boundary layers: First, the continuous spectrum (including entropy wave modes, vorticity wave modes, and acoustic wave modes) and discrete spectrum are obtained via linear stability theory, and the eigenspectrum can be classified into two categories (entropy modes and vorticity modes) according to the modal properties, followed by the resolution of the transient growth process based on optimal perturbation analysis. The results show that the dominant eigenspectrum modes of the two mechanisms differ significantly: The dominant mode of the lift-up mechanism is the entropy/vorticity wave continuous spectrum, within which entropy and vorticity modes jointly dominate; their coupling gain is much higher than that of individual modes, and increasing the spanwise wavenumber can enhance their contribution to transient growth. The dominant mode of the Orr mechanism is the discrete spectrum, where the entropy/vorticity wave continuous spectrum plays a weak role, and transient growth is only related to entropy modes; increasing the streamwise wavenumber can strengthen its effect. In the Mach number range of 0.1 ~ 6, the increase in Mach number (compressibility) exerts a certain inhibitory effect on transient growth, but the type of dominant modes remains almost unchanged. Meanwhile, it increases the number of entropy modes and decreases the number of vorticity modes, weakening the coupling gain of entropy and vorticity modes—this may be one of the reasons for the attenuation of transient growth at high Mach numbers. The corresponding relationship between transient growth mechanisms and modes revealed in this study facilitates understanding of the intrinsic structure and composition of optimal perturbations.