Model of Distributed Receptivity to Kinetic Fluctuations in High-Speed Boundary Layers

Abstract

The receptivity of high-speed compressible boundary layers to kinetic fluctuations is considered within the framework of fluctuating hydrodynamics. The formulation is based on the idea that KF-induced dissipative fluxes may lead to the generation of unstable modes in the boundary layer. Fedorov and Tumin (“Receptivity of High-Speed Boundary Layers to Kinetic Fluctuations,” AIAA Journal, Vol. 55, No. 7, 2017, pp. 2335–2348) solved the receptivity problem using an asymptotic matching approach, which used a resonant inner solution in the vicinity of the neutral point. This study adopts a method of multiple scales approach, which requires fewer assumptions about the locus of primary excitation. The approach is modeled after the one taken by Luchini (“Receptivity to Thermal Noise of the Boundary Layer over a Swept Wing,” AIAA Journal, Vol. 55, No. 1, 2017, pp. 121–130) to study low-speed incompressible boundary layers over a swept wing. The new framework is used to study examples of high-speed flat plate boundary layers whose spectra exhibit nuanced behavior near the generation point, such as first-mode instabilities and near-neutral evolution over moderate length scales.