Stochastic receptivity of laminar compressible boundary layers: An input-output analysis

This study extends the input-output framework for the receptivity analysis of an incompressible boundary layer introduced by Ran et al. [Phys. Rev. Fluids 4, 093901 (2019)] to the laminar adiabatic supersonic case. Spatially distributed in the wall-normal direction, a 8-correlated Gaussian noise is considered as input, both including the velocity and temperature fields. Similarly, components of the resulting velocity and/or temperature fields are chosen as outputs. To study effects on the boundary layer, the measurements of the output are restricted within the 899 boundary layer thickness, implying, however, that effects like acoustic radiation to the free stream are outside the scope of the present analysis. The main goal of the study is twofold: first, to demonstrate the potential of the chosen approach by comparison with familiar results, and second, to extend the current state of knowledge in the compressible regime in selected points by exploiting the extended capabilities of the chosen framework. To this end, the importance of the different inputs???especially the temperature effects???for the amplification of two-dimensional, oblique flow structures and streaks are discussed. Furthermore, the influence of first and second Mach modes (not present in the incompressible regime) is identified within the stochastic framework and results are discussed in light of previous receptivity analyses where the output is restricted to a single mode. By varying the spatial distribution of the forcing, the dependence of the receptivity on the wall-normal position, where the forcing is introduced, is illustrated and discussed. Finally, dominant coherent structures are identified by evaluating the first singular vector of the correlation matrix (proper orthogonal decomposition (POD) modes). By analyzing the dependence of both forcing and response POD modes on the choice of the measured component, further insight is provided about the contribution of temperature fluctuation to the stochastically maintained variance of the system.