Multimode Decomposition in Compressible Boundary Layers

Abstract

Two-dimensional spatially growing perturbations in a two-dimensional compressible boundary layer are considered within the scope of linearized Navier-Stokes equations. Because a spatially growing solution can be expanded into a biorthogonal eigenfunction system, the latter can be utilized for decomposition of flow fields derived from computational studies when pressure, temperature, and all velocity components, together with their derivatives, are available. The method can be used also in a case where partial data are available when a priori information leads to consideration of a finite number of modes. Nomenclature (, , ) x y t A = vector-function of 9 components j A = j-th component of vector A D = d dy 2/ 3 e = ratio of the bulk viscosity to the dynamic viscosity , ij ij