Incompressible Boundary Layer Instability and Transition

The present thesis is an attempt to use classical hydrodynamic stability theory based on a Fourier decomposition of a perturbation around a steady flow solution denoted as the baseflow, and investigate its implications for laminar-turbulent transition modelling. We aim at further bridging the gap that has existed in fluid dynamics for many decades between stability theory and the development of Navier-Stokes solvers. A gap which has been narrowed during the last decade due to advances in nonlinear stability analysis on one side and direct numerical solutions on the other. In particular the nonlinear Parabolized Stability Equations (PSE) will be applied to capture secondary instability waves, the last distinct feature of many unsteady boundary layer flows prior to transition to turbulence.

The historical singularity of parabolic boundary layer solvers that is encountered at a boundary separation point, will affect the PSE in a likewise manner leading to failure of the solution procedure. We try to remedy this shortcoming and shed light into the mechanism that governs the transition in a boundary layer recirculation bubble, introducing for that purpose the Elliptic Stability Equations (ESE).

As a prerequisite to the work outlined above powerful discretization tools must be available. For this purpose a suite of novel 6’th order accurate coupled compact finite difference and finite volume based solvers have been developed in one and two dimensions.