CAREER: Information-Theoretic Approach to Turbulence: Causality, Modeling & Control

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Many flows of engineering interest are dominated by the presence of turbulence, which is the chaotic and multiscale motion of fluids. To date, real-world turbulence limits our ability to fully understand, model, and control complex systems. The lack of a rigorous framework to evaluate cause-and-effect interactions in turbulence is a cross-cutting concept at the core of discovery. The goal of the present proposal is to advance the field of turbulence research by reformulating the problems of causality, modeling, and control using information theory or the science of message communication. In this new framework, turbulence is envisioned as a sequence of bits, and its dynamics is characterized by the transfer of bits among flow variables. The theoretical foundations of this project will provide a new perspective to tackle problems in turbulence research ranging from aircraft aerodynamics to geophysical and planetary flows. The project will also leverage transformative programs to promote diversity and inclusion in engineering, including the participation in annual summer research programs and undergraduate research opportunities to engage women and underrepresented minorities.The goal of this project is to formulate the problems of causality, modeling, and control for turbulent flows using information theory. The central quantity of the formulation is the Shannon entropy, which measures the amount of information in the states of the system. Within this framework, causality in a turbulent flow can be quantified by the information flux among the variables of interest. Reduced-order modeling is posed as a problem on the conservation of information, in which models aim at preserving the maximum amount of information from the original system. Similarly, control theory can be cast in information-theoretic terms by envisioning the tandem sensor-actuator as a device reducing the unknown information of the state to be controlled. This new formulation will be exploited to advance three outstanding problems in turbulent flows: (i) causality of the energy transfer in the turbulent cascade, (ii) subgrid-scale modeling for large-eddy simulation, and (iii) suppression of turbulent separation bubbles with active flow control. The cases of study range from canonical flat plate turbulence to complex flows such as realistic aircraft configurations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.