Initial Conditions, Sensitivity, and Robustness for Statistical Modeling of Transition*

In this talk, we address the question: how well can the transition process be described by a small number of single-point statistics? Closure models for turbulence assume that the state of the flow can be sufficient characterized by a small number of statistics: two second-order moments for k- ? and seven for a full Reynolds-stress transport model. Experimental observation suggests that transition may exhibit a much greater sensitivity to perturbations of the initial conditions. Such a sensitivity would be a fundemental limitation on any future statistical theory of transition.

Direct numerical simulation of Taylor-Green like initial conditions show that initial conditions with very low levels of noise transition along highly specific trajectories, which are quite different from typical broad-spectrum forcing. At higher noise levels, the results are much less sensitive to perturbations. These results have important implications for transition modeling.