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**Venue:** Zoom Event

**About Baole Wen:** Dr. Wen obtained a B.S. degree in Engineering Mechanics and a M.S. degree in Fluid Mechanics, respectively, from the Beijing University of Aeronautics and Astronautics. He was awarded a CEPS Graduate Fellowship \& a Dissertation Year Fellowship and earned a Ph.D. in Applied Mathematics from University of New Hampshire in 2015. His Ph.D. research was focused on understanding the underlying flow and transport mechanisms governing the spatiotemporally-chaotic system of porous medium convection at large Rayleigh numbers. Upon graduation, he was awarded a Peter O’Donnell, Jr. Postdoctoral Fellowship through the Oden Institute for Computational Engineering and Sciences in the University of Texas at Austin. His primary research interests are fluid dynamics, mathematical modeling, scientific computing and dynamical systems theory. Recently, he is working with Dr. Charles Doering as a Postdoctoral Assistant Professor at University of Michigan on extreme behavior in fundamental models of fluid mechanics.

**STEADY COHERENT STATES IN RAYLEIGH–B\'{E}NARD CONVECTION: **Buoyancy-driven flows are central to engineering heat transport, atmosphere and ocean dynamics, climate science, geodynamics, and stellar physics. Rayleigh–B\’enard convection—the buoyancy driven flow in a fluid layer heated from below and cooled from above—is recognized as the simplest scenario in which to study such phenomena, and beyond its importance for applications this problem has served for a century as one of the primary paradigms of nonlinear physics, complex dynamics, pattern formation and turbulence. A central question about Rayleigh–B\’enard convection is how the Nusselt number $Nu$ depends on the Rayleigh number $Ra$ and the Prandtl number $Pr$—i.e., how heat flux depends on imposed temperature gradient and the ratio of the fluid’s kinematic viscosity to its thermal diffusivity—as $Ra\rightarrow\infty$. Experiments and simulations have yet to rule out either `classical’ $Nu \sim Ra^{1/3}$ or `ultimate’ $Nu \sim Ra^{1/2}$ asymptotic scaling. Here we provide clear quantitative evidence suggesting that the ultimate regime might not exist. Our tactic is to study relatively simple time-independent states called rolls and compare heat transport by these rolls with that of turbulent convection. These steady rolls are not typically seen in large-$Ra$ simulations or experiments because they are dynamically unstable. Nonetheless, they are part of the global attractor for the infinite-dimensional dynamical system defined by Rayleigh’s model, and recent results suggest that steady rolls may be one of the key coherent states comprising the `backbone’ of turbulent convection. By developing novel numerical methods, we compute steady rolls between no-slip boundaries for $Ra\le 10^{14}$ with $Pr=1$ and various horizontal periods. We find that rolls of the periods that maximize $Nu$ at each $Ra$ have classical $Nu\sim Ra^{1/3}$ scaling asymptotically, and they transport more heat than turbulent experiments or simulations at similar parameters. If turbulent heat transport continues to be dominated by steady transport asymptotically, it cannot achieve ultimate scaling.

The MICDE Fall 2020 and Winter 2021 Seminar Series is open to all. University of Michigan faculty and students interested in computational and data sciences are encouraged to attend.

This event will be a joint seminar with the University of Michigan Applied Interdisciplinary Mathematics.

Questions? Email MICDE-events@umich.edu

Join the webinar via the Zoom details below:

https://umich.zoom.us/j/96450383843

Meeting ID: 964 5038 3843

Passcode: 010182