Stability Analysis of Turbulent Fluid Flow

Hydrodynamic stability refers to the study of when and how laminar flows transition to turbulence. This includes investigations of the mechanisms of transition, as well as the classification of known flow configurations as either stable or unstable and the identification of critical values of flow parameters at which this bifurcation occurs. In this thesis, we introduce the mathematical theory behind continuum mechanics and fluid dynamics as well as some tools from the study of dynamical systems. We apply these concepts to the linear stability analysis of zero pressure gradient flat plate flow via numerical simulations in OpenFOAM, discussing both the theoretical and numerical issues. We use the Arnoldi iteration method to solve for the leading eigenvalues at the critical value of the Reynolds number parameter. We conclude by discussing the prospect of using topological data analysis to characterize flow snapshots in real time.