The Presidential Young Investigator will continue working on several problems in the general area of fluid transport. The first area involves the study of fluid stability; in particular, Bayly will try to extend results on broadband instability from two dimensions to three dimensions. The goal of this research is to develop a global picture of instability modes and hence, a coherent picture of broadband instabilities in general flows. The second area involves the magnetohydrodynamic (MHD) dynamo problem; in particular, the investigator and a colleague at NYU will try to discover what is needed to produce a fast dynamo. Their strategy is to perform high-resolution MHD simulations of dynamo actions and establish rigorous error bounds on the numerical discretizations. Various types of fluid dynamical phenomena involve the creation and evolution of instabilities. An instability is produced when a small or large perturbation upsets an existing balance of forces and leads to the formation of a new equilibrium state, which in turn might itself change in response to new perturbations. It is easy to imagine that one is interested in such changes in equilibrium states, since the design of apparatus depends crucially upon what the prevailing equilibrium state is thought to be in a given flow situation. The investigator will use analytical and computational tools to describe the evolution of broadband instabilities in complex flows and the impact of relatively large disturbances.
