We recommend that non-UIC participants attend online. Any non-UIC participants who would like to attend in-person events need to register with the organizer at least three days before the seminar. If you have any questions, please contact Eloy Reyes.

Analysis and Applied Mathematics Seminar

Anuj Kumar
UC Santa Cruz
Optimizing scalar transport with branching pipe flows
Abstract: We consider the variational problem of "optimal wall-to-wall transport", in which we look to maximize the transport of a passive temperature field between hot and cold plates. Specifically, we optimize the choice of divergence-free velocity field in the advection-diffusion equation, amongst all velocities satisfying an enstrophy constraint. Previous work established an a priori upper bound to transport, scaling as the 1/3 power of the flow’s enstrophy (i.e., the power used to make the flow). Recently, Tobasco and Doering '17 constructed self-similar two-dimensional branching flows saturating this bound up to an unknown logarithmic correction to scaling. We present a three-dimensional "branching pipe flow" that eliminates the possibility of this logarithmic correction, and therefore identifies the optimal scaling as a clean 1/3 power law. Our flows resemble previous numerical studies of the three-dimensional wall-to-wall problem (Motoki, Kawahara and Shimizu ’18), but actually we show using a time-dependent version of our construction that the 1/3 scaling is in fact optimal in two-dimensions as well. These results have natural connections to the outstanding problem of Rayleigh--Bénard convection, and we propose several conjectures along these lines.
Monday February 14, 2022 at 4:00 PM in 636 SEO
Web Privacy Notice HTML 5 CSS FAE
UIC LAS MSCS > persisting_utilities > seminars >