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Interactions of large amplitude solitary waves in viscous fluid conduits

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journal contribution
posted on 10.03.2015 by Nicholas K. Lowman, M.A. Hoefer, Gennady El
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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

JOURNAL OF FLUID MECHANICS

Volume

750

Pages

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 Press

Version

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

2014

Notes

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

ISSN

0022-1120

Language

en

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