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Multiple solutions in free surface flows

Banff International Research Station for Mathematical Innovation and Discovery

The presence of a free-surface between air and liquid can lead to nonlinear behaviour, even in the absence of fluid inertia. Consequently, multiple distinct flow states may occur under the same driving conditions. A natural question to ask is whether simplified models of the system can capture the correct nonlinear behaviour, compared to the full field equations. For the (canonical) flow of a liquid film on the inner, or outer, surface of a rotating cylinder, we find multiple solutions and other complex behaviours can be accurately described over a wider range of parameters using a simplified model system derived via gradient dynamics rather than strict asymptotic arguments. (Joint work with Andre Von Borries Lopes and Uwe Thiele.)

Mathematics; Fluid mechanics; Approximations and expansions; Fluid dynamics

video/mp4

Author affiliation: University of Manchester

2019-10-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72119

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/