Characterization, modeling, and control of turbulence from a network-theoretic perspective
Abstract
Turbulent flows are ubiquitous in engineering and science, and there is great interest in modifying the behaviors of such flows to enhance mixing, reduce drag, and improve fuel efficiency for various fluid based engineering systems. Analyzing and controlling turbulent flows is difficult due to the rich high-dimensional complex vortex dynamics with strong nonlinear interactions that take place over a broad range of length and time scales. To improve our ability to modify turbulent fluid flows, the current computational and theoretical study proposes to perform interaction-based characterization and control of canonical turbulent flows by taking advantage of network theory. A fluid flow network can be described as a complete graph with edge weights having a wide range of scales. In fact, our preliminary findings show that the complex vortical interactions in isotropic turbulence can be described by a weighted scale-free network. To capture the essence of the flow interactions while achieving global conservation properties, we will model the complex fluid flow by reducing the dimension of the state variables using concepts from Reduced-Order Modeling (ROM) and further extracting the dominant interactions present in the physics using our Sparsified Dynamics Model (SDM). By combining these two approaches, we will be able to achieve a sparse lower-order representation of the turbulent flow fields using network-based techniques. Once the sparse network-based model of turbulent fluid flow is established, we will perform open and closed-loop control of the dominant structures in turbulent flows of interest. Instead of full structural control of every node, or eddy, in the flow, we are interested in the degree of controllability of large-scale coherent structures. We will therefore investigate the controllability of scale-free turbulence networks using techniques from balanced model reduction and the aforementioned network-based techniques. In particular, we will extend dynamic mode decomposition (DMD) to network contexts. Recent innovations of DMD/Koopman analysis with control will provide insights into spatial-temporal coherent structures in the fluid network and will enable advanced nonlinear control. We will consider a number of candidate turbulent flow problems to apply the aforementioned network-based analysis and control techniques. These problems will be selected to highlight the dynamic behavior of fluid flows on networks and test the effectiveness of the developed controllers. In particular, we will examine high-dimensional networked ODE models such as the Kuramoto oscillator network (which captures fundamental behavior of unsteady flows), two and three-dimensional isotropic turbulence, and wall-bounded turbulent flows. These problems play fundamental roles in fluid mechanics, which can lead to broader impacts in how turbulent flows in general can be modeled and controlled. The findings and developments from the proposed e ort should bring rise to a new approach in controlling the global behavior of turbulent flows by modifying the interaction network of turbulent vortices, complementing traditional active turbulence control e orts. We foresee that the proposed effort will not only lay a pathway for the control of continuum systems, but also for other high-dimensional dense networks with complex dynamics.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 14, 2019
- Source ID
- W911NF1910032
Entities
People
- Kunihiko Taira
Organizations
- Army Contracting Command
- United States Army
- University of California, Los Angeles