Investigations of boundary layer transition via Galerkin projections on empirical eigenfunctions

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Abstract
In this paper, Galerkin projections on eigenfunctions as obtained by proper orthogonal decomposition of numerically computed flow fields are used to derive dynamical models for different regions of a transitional boundary layer. The regions investigated cover the stages of the transition process from the evolution of low-amplitude Tollmien-Schlichting waves up to the final stages of transition, right at the onset of turbulence. In a first part of the paper, the possibilities and limitations of the approach chosen are investigated in detail, and in a second part the application of the techniques developed before is demonstrated for the case of a spatially evolving boundary layer that is inhomogeneous in all spatial directions. The focus of this work is mainly on how characteristic properties of the dynamics change as transition evolves in the streamwise direction.