conduit_soli_interacts.pdf (900.68 kB)
Interactions of large amplitude solitary waves in viscous fluid conduits
journal contribution
posted on 2015-03-10, 16:24 authored by Nicholas K. Lowman, M.A. Hoefer, Gennady ElThe free interface separating an exterior, viscous fluid from an intrusive conduit of buoyant, less viscous fluid is known to support strongly nonlinear solitary waves due to a balance between viscosity-induced dispersion and buoyancy-induced nonlinearity. The overtaking, pairwise interaction of weakly nonlinear solitary waves has been classified theoretically for the Korteweg–de Vries equation and experimentally in the context of shallow water waves, but a theoretical and experimental classification of strongly nonlinear solitary wave interactions is lacking. The interactions of large amplitude solitary waves in viscous fluid conduits, a model physical system for the study of one-dimensional, truly dissipationless, dispersive nonlinear waves, are classified. Using a combined numerical and experimental approach, three classes of nonlinear interaction behaviour are identified: purely bimodal, purely unimodal, and a mixed type. The magnitude of the dispersive radiation due to solitary wave interactions is quantified numerically and observed to be beyond the sensitivity of our experiments, suggesting that conduit solitary waves behave as ‘physical solitons’. Experimental data are shown to be in excellent agreement with numerical simulations of the reduced model. Experimental movies are available with the online version of the paper.
History
School
- Science
Department
- Mathematical Sciences
Published in
JOURNAL OF FLUID MECHANICSVolume
750Pages
372 - 384 (13)Citation
LOWMAN, N.K., HOEFER, M.A. and EL, G.A., 2014. Interactions of large amplitude solitary waves in viscous fluid conduits. Journal of Fluid Mechanics, 750, pp.372-384.Publisher
© Cambridge University PressVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2014Notes
This paper was accepted for publication in the Journal of Fluid Mechanics and the definitive published version is available at: http://dx.doi.org/10.1017/jfm.2014.273ISSN
0022-1120Publisher version
Language
- en