  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.
