Getting to the Core of Vortex Mechanics: A Hybrid Experimental and Numerical Study of Twist, Shear, and Wall Interactions

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Concentrated vortices are ubiquitous in fluid mechanics; examples include tornadoes, turbulence, and flows around aerodynamic surfaces like wings. As a result, simplified models of vortex behavior have long been used to understand their basic motion and properties. Unfortunately, these models are far too simple to explain many real-world phenomena because they neglect features like the internal structure of the vortex and coupling to other flows. This project will develop new vortex models which include these features and validate them using a unique combination of experiments and numerical simulations. Ultimately, the aim of these models is to provide an intuitive picture of vortex mechanics that allows improved prediction and control of fluid behavior in a wide range of contexts. The project also includes a significant educational component, including research opportunities for graduate and undergraduate students, as well as an outreach program designed to promote scientific education and increase participation of underrepresented groups in STEM fields.Due to the ubiquity of compact vortex cores in high Reynolds number flows, vortex mechanics is widely studied in physics, engineering, and applied mathematics. Previous work on vortex geometry and topology has shown that it is a powerful tool for understanding many phenomena in fluid mechanics. This project aims to extend this analysis to a much wider range of flows by incorporating core details and wall/shear interactions into existing vortex filament models. These models will be validated in two complementary ways: (1) experiments using streamwise vortices shed into pipe flow and (2) direct numerical simulations of the experiments and simplified flows designed to test specific aspects of the models. Although the research program will focus on a narrow set of example flows, the example cases are designed to uncover fundamental interaction mechanisms between vortices, walls, and shear flows. Building on previous research on the role of vortex geometry and topology for isolated vortices, it should then be possible to study the dynamics and transport of quantities like energy, helicity, and enstrophy in terms of the shape of the vortex lines and their alignment with respect to background flows. If successful, this will enable future studies of more complicated flows of many tangled vortices, greatly expanding the reach of a vortex-based understanding of fluid mechanics. In addition, new mathematical modeling tools (including open-source code) will be developed that could be applied to many open problems in fluid mechanics, such as the turbulent transition or tornado formation.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.