Receptivity to kinetic fluctuations: A multiple scales approach

The receptivity of high-speed compressible boundary layers to kinetic fluctuations (KF) 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 Tumin¹ (AIAA J., 2017) solved the receptivity problem using an asymptotic matching approach which utilized a resonant inner solution in the vicinity of the neutral point of the second Mack mode. Here we adopt a slightly more general inhomogeneous multiple scales (IMS) approach, based on a WKB ansatz, which requires fewer assumptions about the locus of primary excitation. The approach is modeled after the one taken by Luchini² (AIAA J., 2017) to study low speed incompressible boundary layers over a swept wing. The new framework is used to study examples of high-speed, high-enthalpy, flat plate boundary layers (see Edwards and Tumin³) whose spectra exhibit nuanced behavior near the generation point, such as first Mack mode instabilities and near-neutral evolution over moderate length scales.