Three-Dimensional Spatial Normal Modes and Multimode Decomposition for Reacting Boundary Layers

Three-dimensional spatially growing perturbations within a two-dimensional boundary layer in a binary mixtures of reacting gases are considered within the scope of the linearized compressible reacting flow equations. The corresponding spatial Cauchy problem for disturbances is solved and shown to be computable in terms of a corresponding biorthogonal eigenfunction system. To solve the Cauchy problem, key parts of the spectrum such as the continuous spectrum are analyzed in detail. Particular attention is placed on interpreting compositional branches of the continuous spectrum and potential resonant interactions with discrete modes. These results are then used to solve a compositional spot receptivity problem motivated by potential resonant interactions between discrete modes and compositional branches of the continuous spectrum. It is then shown how the same framework can be conveniently used to decompose perturbation flow field data in a chemically reacting mixture.