Mathematical Sciences: Stability of Streak-like Structures in Wall-bounded Shear Flows

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9406636 Schmid A great number of turbulent fluid flows show the presence of streak-like elements in the near-wall region. These coherent fluid patterns, and in particular their persistence and flow-independent scales, have stimulated a great deal of interest and investigations among the fluid dynamic community. Although it has been found that their appearance and dynamics play a crucial role in the transition to turbulence and in fully developed turbulence, our knowledge about streaks in wall-bounded shear flows is rather limited despite remarkable progress over the past years. The present proposal aims at investigating the dynamics of streaks as well as their role in the production and sustainment of turbulent fluid motion by a nonlinear stability analysis. Owing to experimental and computational evidence, special emphasis will be directed toward the important phase of the breakdown of streak-like structure. A combined theoretical and numerical approach will be taken, employing a Floquet stability analysis where the primary finite-amplitude disturbance state will consist of a (slowly decaying) streamwise vortex. The resulting stability equations for three-dimensional secondary disturbances will then be treated within a temporal and spatial framework using both asymptotic, eigenvalue-based tools and transient, initial-value-based techniques. Direct numerical simulations will be conducted to complement and scrutinize the theoretical results. The emphasis of this project will be on the influence of flow parameters on the overall stability behavior and on the complete description of the dynamics of the breakdown process.