AM Seminar: Heat Transport and Scalar Dissipation in Turbulent Flows: A Constructive Approach

Presenter: Anuj Kumar, Assistant Professor, UC Davis

Description: Turbulent flows can transport heat and momentum much more efficiently than pure molecular diffusion alone. What flow structures enable this efficient transport and how can they sustain dissipation when diffusivity or viscosity is small? These questions are fundamental to understanding turbulence and have important applications in engineering. In this talk, I will discuss a constructive approach to these questions through explicitly designed incompressible flows. We will first consider heat transport between walls held at different temperatures. Under a constraint on the power supply, I will present a three dimensional branching construction that achieves the optimal heat transport scaling. By examining these designs carefully, we will identify the physical mechanisms responsible for efficient heat transfer and discuss potential applications, including the pressing problems of cooling in AI data centers. We will then turn to scalar turbulence. I will introduce a universal incompressible flow built from a carefully organized hierarchy of shear flows and explain how these constructions approach the sharp Obukhov–Corrsin regularity threshold for scalar dissipation. These constructions also exhibit eddy-diffusivity effect: advection mimics diffusion of order one even in the transport equation, where molecular diffusion is entirely absent. Together, these examples illustrate how the process of constructing flows that achieve sharp scaling laws can also reveal the mechanisms underlying enhanced transport and dissipation, which are two key features of turbulence.

About the speaker: Anuj Kumar is an Assistant Professor in the Department of Mathematics at the University of California Davis. His research lies at the intersection of fluid dynamics, partial differential equations (PDEs) and applied mathematics, combining computational, mathematical analysis and theoretical approaches. Prior to joining UC Davis, he was a Visiting Assistant Professor in the Department of Mathematics at the University of California Berkeley. He earned my Ph.D. in Applied Mathematics from the University of California Santa Cruz in 2023.

This seminar is hosted by Professor Pascale Garaud.