Bulk Properties and Flow Structures in Turbulent Flows*

Turbulence, characterized by unsteady, irregular, and chaotic fluid motion, is ever-present in natural and engineering flows. The two major lines of investigation in turbulent flows are (1) the study of emergent bulk properties such as drag, energy dissipation, and heat and mass transport, (2) qualitative and quantitative analysis of flow structures. I will present a few key findings from my Ph.D. research, which integrates ideas from engineering, physics, and mathematical analysis. First, I will discuss obtaining rigorous bounds on turbulent bulk quantities that are valid in extreme parameter regimes, relevant to many engineering, geophysical, and astrophysical flows. The second part is dedicated to designing simple flows, steady or time-periodic, that effectively mimic the most important characteristics of turbulent flows. One such problem is related to the design of forcing in the Navier–Stokes equation such that the resultant flow maximizes the heat transfer between two differentially heated walls for a given power supply. I will present a novel construction of 3D branching pipe flows and demonstrate that these flows are the most efficient in transporting heat. I will conclude with a discussion of the broader impacts of my research and exciting future directions.