Abstract

Enhanced dissipation is a phenomenon of central interest in both physics and mathematics due to its fundamental role in fluid mixing and its applications across various industries, particularly in chemical processes. Over the past two decades, significant advances in mathematical fluid mechanics have led to rigorous descriptions of this effect, providing precise quantitative estimates of energy dissipation rates for certain classes of flows (Constantin, Kiselev, Ryzhik & Zlatos 2008; Bedrossian & Coti-Zelati 2017; Coti-Zelati, Delgadino & Elgindi 2019). However, due to the complexity of the dynamics generated by time dependent velocity fields and the limitations of existing bounding techniques, quantitative studies for this class of flows remain more challenging and less explored. In this talk, I will present recent joint work with Johannes Benthaus on quantitative bounds for time-dependent shear flows that exhibit (super-)enhanced dissipation. Some of our results are inspired by mixing mechanisms commonly used in analytical laboratories, providing insights into how specific flow structures can drastically accelerate dissipation. I will also discuss our extension to intermittent flows and highlight connections with problems in control theory.