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Title: Interactions of large amplitude solitary waves in viscous fluid conduits
Authors: Lowman, Nicholas K.
Hoefer, M.A.
El, G.A.
Keywords: Pattern formation
Solitary waves
Stokesian dynamics
Issue Date: 2014
Publisher: © Cambridge University Press
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.
Abstract: The 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.
Description: 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.2014.273
Version: Accepted for publication
DOI: 10.1017/jfm.2014.273
URI: https://dspace.lboro.ac.uk/2134/16944
Publisher Link: http://dx.doi.org/10.1017/jfm.2014.273
ISSN: 0022-1120
Appears in Collections:Published Articles (Maths)

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