Numerical Simulation and Theoretical Analysis of Perturbations in Hypersonic Boundary Layers

T HE progress being made in computational fluid dynamics provides an opportunity for reliable simulations of such complex phenomena as laminar-turbulent transition. The dynamics of flow transition depends on the instability of small perturbations excited by external sources. Computational results provide complete information about the flowfield that would be impossible to measure in real experiments. Recently, amethod of normalmode decompositionwas developed for twoand three-dimensional perturbations in compressible and incompressible boundary layers [1–3]. In [4], the method was applied to the theoretical analysis of a perturbation flowfield in the vicinity of a blowing–suction actuator obtained from direct numerical simulation (DNS). The results demonstrated very good agreement between the amplitudes of the modes filtered out from the DNS data and those solved by linear theory of the flow receptivity to wall blowing–suction. However, the development of the perturbations downstream from the actuator has not been analyzed yet. Perturbations observed in experiments and computations in the vicinity of an actuator possess a nonmonotonic character. This behavior occurs because the perturbation introduced by the actuator is composed ofmodes of the discrete (unstable and stablemodes) and continuous spectra, and one cannot distinguish the unstable mode clearly. Are the observations still compatible with the linear stability theory (LST)? To answer this question, we must decompose the perturbation into the normal modes and compare their amplitudes with those predicted by LST. However, the LST prediction must take into account the nonparallel boundary-layer flow effects, because the development of the perturbation takes place on a length scale much larger than the boundary-layer thickness. The nonparallel flow effects on the development of unstable discrete modes on a length scale that is much larger than the boundary-layer thickness have been studied within the scope of the method of multiple scales (MMS) [5–13]. Another method that allows inclusion of the nonparallel flow effects on unstable modes is based on the parabolized stability equations [14–16]. Fedorov and Khokhlov [17] pointed out that the role of decaying modes can be significant, and one must pay attention to them if there is a synchronismwith the other modes. Because the analysis of decaying modes is important, onemust include the nonparallel boundary-layer flow effects using the MMS. In the present work, we apply the multimode decomposition to DNS results downstream from the blowing–suction actuator in hypersonic boundary layers past a flat plate and a sharp wedge to compare the amplitudes of the modes found from the computations with the prediction of the LST including nonparallel flow effects.