CAREER: Scale-dependent reduced-order models for turbulent flows

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Turbulent flows are ubiquitous in science and engineering, and their wide range of spatial and temporal scales make them simultaneously expensive to simulate and challenging to model. Effective reduced-order models that can be used in place of costly simulations are urgently needed to accelerate scientific discovery, engineering design, and control of turbulent flows. This project will fill this need by developing a new class of reduced-order models that, by respecting key aspects of turbulent flow physics, overcome longstanding limitations of previous methods. These new tools will be applicable to a wide range of turbulent flows and can be applied by researchers in academia, government labs, and industry to achieve objectives such as preventing the adverse health effects of excessive noise exposure by mitigating acoustic emissions of jet engines and wind turbines and improving our understanding of climate change by enhancing predictive modeling capabilities of geological flows. The research program is closely integrated with a comprehensive education program, the central component of which is a series of professionally produced videos, each spotlighting a key contributor to the field of fluid dynamics and the impactful problems they work on. By highlighting a diverse set of researchers and focusing on not just the science, but also the scientist, the videos will help empower students from underrepresented populations to envision themselves as future fluid-dynamics researchers, broadening participation in STEM and diversifying the workforce. The technical goal of the project is to develop a pair of new models tailored for long- and short-time prediction of turbulent flows. The critical observation is that typical reduced-order models based on expansion of the flow state into spatial modes and time-varying coefficients, such as standard Galerkin models and their modern alternatives, violate the intimate physical relationship between spatial and temporal scales of the flow. By working within a nascent space-time modeling framework, in which the flow state is expanded into modes that depend on both space and time, and strategically selecting the temporal basis functions, the proposed approach respects the physical relationship between spatial and temporal scales. Critical tasks to bring this framework to maturation include developing optimal spatial bases, sparsifying triadic nonlinear interactions, and deriving error estimates. To accelerate and streamline their adoption, the methods developed during this project will be incorporated into the open-source platform Pressio maintained by Sandia National Laboratory.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.