Olivier Devauchelle - Boltzmann statistics in alluvial rivers
| Dates: | 18 November 2020 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Olivier Devauchelle (IPGP) joins us for this virtual seminar in the Physical Applied Mathematics Series
This seminar will be held via Zoom. Please email alice.thompson@manchester.ac.uk if you require the meeting details.
Boltzmann statistics in alluvial rivers
Devauchelle, P. Popovic, A. Abramian & E. Lajeunesse.
Obviously, rivers transport water. Often, they also carry the sediment their bed is made of; they are then called "alluvial". This means that they build themselves through the coupling of the water flow to the sediment flux it induces.
At its simplest, this fluid-structure interaction involves a granular bed, and a fluid flow strong enough to move the grains. We produce a laboratory version of it by pouring a viscous fluid over a layer of plastic sediment, until a small river appears, and reaches its steady state. Tracking the traveling grains with a camera, we find that their erratic motion makes them diffuse across the stream. The equilibrium between this macroscopic diffusion and gravity is analogous to that of a column of gas submitted to gravity.
What sets laboratory rivers apart from classical statistical physics, however, is their ability to change the potential that confines the traveling grains. This ability relates the Boltzmann-like distribution of the traveling grains to the channel's cross section. We formalize this relation with a non-linear equation reminiscent of the Liouville-Bratu-Gelfand equation. Some of its solutions match our experiments, and resemble natural rivers.
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