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Title: Generation of undular bores in the shelves of slowly-varying solitary waves
Authors: El, G.A.
Grimshaw, Roger H.J.
Issue Date: 2002
Abstract: We study the long-time evolution of the trailing shelves that form behind solitary waves moving through an inhomogeneous media, within the framework of the variable-coeffecient Korteweg-de Vries equation. We show that the nonlinear evolution of the shelf leads typically to the generation of an undular bore and an expansion fan, which form apart but start to overlap and nonlinearly interact after a certain time interval. The interaction zone expands with time and asymptotically as time goes to infinity occupies the whole perturbed region. Its oscillatory structure strongly depends on the sign of the inhomogeneity gradient of the variable background medium. We describe the nonlinear evolution of the shelves in terms of exact solutions to the KdV-Whitham equations with natural boundary conditions for the Riemann invariants. These analytic solutions, in particular, describe the generation of small 'secondary' solitary waves in the trailing shelves, a process observed earlier in various numerical simulations.
Description: This pre-print has been submitted, and accepted, to the journal, Chaos. The definitive version: EL, G.A. and GRIMSHAW, R.H.J., 2002. Generation of undular bores in the shelves of slowly-varying solitary waves. Chaos, 12(4), pp. 1015-1026, is available at: http://chaos.aip.org/chaos/.
URI: https://dspace.lboro.ac.uk/2134/451
Appears in Collections:Pre-prints (Maths)

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