Global receptivity analysis: physically realizable input-output analysis

TL;DR

This paper introduces a physically realizable input-output analysis framework for transition in high-speed flows, improving the understanding of disturbance amplification and transition mechanisms by incorporating realistic disturbance constraints.

Contribution

The authors develop a scattering formalism that restricts disturbances to physically realizable outer solutions, filling a gap in traditional worst-case disturbance analysis.

Findings

Validated framework with DNS for Mach 4.5 flow

Identified optimal disturbance combinations for energy amplification

Provided insights into transition mechanisms in supersonic flows

Abstract

In the context of transition analysis, linear input-output analysis determines worst-case disturbances to a laminar base flow based on a generic right-hand-side volumetric/boundary forcing term. The worst-case forcing is not physically realizable, and, to our knowledge, a generic framework for posing physically-realizable worst-case disturbance problems is lacking. In natural receptivity analysis, disturbances are forced by matching (typically local) solutions within the boundary layer to outer solutions consisting of free-stream vortical, entropic, and acoustic disturbances. We pose a scattering formalism to restrict the input forcing to a set of realizable disturbances associated with plane-wave solutions of the outer problem. The formulation is validated by comparing with direct numerical simulations (DNS) for a Mach 4.5 flat-plate boundary layer. We show that the method provides insight into transition mechanisms by identifying those linear combinations of plane-wave disturbances that maximize energy amplification over a range of frequencies. We also discuss how the framework can be extended to accommodate scattering from shocks and in shock layers for supersonic flow.