9706961 Lopez and Shen This project is to study dynamic control and parametric excitations in hydrodynamic systems and to examine the interplay between parametric resonance and stabilization/destabilization of transitions/bifurcations, through an integrated program of analysis, computation and experiment. Two basic flow sets, namely the Taylor-Couette flow and vortex breakdown flow, have been chosen in order to develop a general understanding of the complex hydrodynamics and control strategies. These generic flows are attractive because the degree of complexity can be precisely controlled by relatively simple changes in the flow state or boundary conditions, and at the same time they possess rich dynamics which are representative of a wide class of general hydrodynamic systems that may respond to dynamic control in a complex manner. In particular, these classes of flows may respond resonantly to the parametric excitation of the applied control. An investigation of the behavior of these generic flows will help to form a better understanding of more general time-dependent hydrodynamic systems. The interplay between dynamic control mechanisms and parametric resonance will be investigated using (linear) Floquet theory as a first step in understanding the dynamics at the point of transition or bifurcation. Flows beyond the validity of the Floquet analysis will be studied using three different nonlinear computational approaches, each with distinct advantages and limitations. Their combined implementation is capable of resolving a wide range of problems and addressing distinct issues within each problem. The results from the experiment will be used to refine the analysis and control implementation. This research will not only result in a deeper understanding of the complex spatio-temporal dynamics of hydrodynamic systems, but will also make a significant practical impact. For example, in the aerodynamics industry, the control strategies will aid in drag reduction a nd reduced fatigue due to aero-acoustic structural resonances; in fact, parametric excitation in the form of span-wise oscillations of the boundary has recently been demonstrated experimentally to reduce drag in turbulent boundary layers by researchers at the University of Texas and others. In the materials and chemical processing industries, many of the manufacturing processes rely on an effective control of transitions and instabilities. The new fundamental and practical insights on control dynamics of complex systems anticipated from this research can provide U.S. industry with a competitive edge.
