On the Identification of Nonlinear Optima in Spatially Developing Boundary Layer Flow

Abstract: The present thesis studies transition to turbulence in a spatially developing bound-ary layer for subcritical Reynolds numbers. A fully nonlinear iterative direct-adjoint optimisation technique is employed to identify finite amplitude perturbations triggering transition in an energy efficient way. The study explores two approaches to find the Reynolds number scaling of the subcritical transition energy threshold Ec(Re) and the corresponding nonlinear optimum which is the minimal seed for subcritical transition to turbulence. The first approach focuses on shortened optimisation time horizons T compared to a reference case with T = 400. It is shown that the transition energy threshold Ec increases for T = 200/300 when compared to the reference value Ec,T =400. This is linked to the existence of local optima which maximise the objective functional for short transient times. These local optima are fully localised and feature the Orr and liftup energy growth mechanisms as observed for the reference case. However, their long-time evolution is suboptimal since it leads to a stable streak configuration which is found to relaminarise also for initial amplitudes of E0 > Ec,T =400. The second approach of using an inflow Reynolds number increased by factor 3/2 but non-shortened T is shown to be suitable to identify the scaling Ec(Re). Exploratory optimisation runs suggest a decrease in the transition energy threshold of at leastEc(3/2 · Re)/Ec(Re) < 0.47.