Turbulence, the disorganized motion of a fluid (often associated with a bumpy ride on an airplane), is ubiquitous in science and engineering, impacting everything from the flight of a golf ball, to fuel efficiency and noise of an engine, to the formation of stars. One important tool for studying and modeling turbulent flows is a mathematical framework called resolvent analysis, which identifies energy amplification mechanisms key to generating and sustaining turbulence. Unfortunately, resolvent analysis requires significant computational resources when applied to realistic engineering systems.
The goal of this project is to develop a new algorithm that reduce the cost of resolvent analysis of large systems by several orders of magnitude. This capability could lead to a better theoretical understanding of turbulence and improved design of engineering systems involving turbulent flow. More broadly, the algorithm will also be applicable to problems in other areas of science and engineering, including applied mathematics (where the resolvent operator can be used to solve integral and differential equations), solid mechanics and structural engineering (where the resolvent operator is used to study the frequency response of structures), and controls (where the resolvent operator can be used to design and evaluate controllers).