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Title: Transformation of a shoaling undular bore
Authors: El, G.A.
Grimshaw, Roger H.J.
Tiong, Wei K.
Keywords: Shallow water flows
Solitary waves
Topographic effects
Issue Date: 2012
Publisher: © Cambridge University Press
Citation: EL, G.A., GRIMSHAW, R.H.J. and TIONG, W.K., 2012. Transformation of a shoaling undular bore. Journal of Fluid Mechanics, 709, pp. 371-395.
Abstract: We consider the propagation of a shallow-water undular bore over a gentle monotonic bottom slope connecting two regions of constant depth, in the framework of the variablecoefficient Korteweg – de Vries equation. We show that, when the undular bore advances in the direction of decreasing depth, its interaction with the slowly varying topography results, apart from an adiabatic deformation of the bore itself, in the generation of a sequence of isolated solitons — an expanding large-amplitude modulated solitary wavetrain propagating ahead of the bore. Using nonlinear modulation theory we construct an asymptotic solution describing the formation and evolution of this solitary wavetrain. Our analytical solution is supported by direct numerical simulations. The presented analysis can be extended to other systems describing the propagation of undular bores (dispersive shock waves) in weakly non-uniform environments.
Version: Accepted for publication
DOI: 10.1017/jfm.2012.338
URI: https://dspace.lboro.ac.uk/2134/15334
Publisher Link: http://dx.doi.org/10.1017/jfm.2012.338
ISSN: 0022-1120
Appears in Collections:Published Articles (Maths)

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