On the structure of dynamical systems describing the evolution of coherent structures in a convective boundary layer

Abstract

By Galerkin projection of the Navier–Stokes equations onto a system of empirical eigenfunctions, as obtained using the POD method, systems of ODEs have been derived that model the dynamics of coherent structures in a transitional flat-plate boundary layer. These ODEs are found to approximately exhibit the structure of systems of linear oscillators that are nonlinearly coupled via quadratic interactions. Investigations for different regions of the boundary layer (at different downstream positions) show distinct changes in the eigenfrequencies of these linear oscillators, eventually leading to low-dimensional chaos at the onset of turbulence.