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Download fileUnsteady undular bores in fully nonlinear shallow-water theory
preprint
posted on 2005-08-15, 11:20 authored by Gennady El, Roger Grimshaw, Noel F. SmythWe consider unsteady undular bores in the fully nonlinear dissipationless shallow-
water dynamics described by the Green-Naghdi system. We use the Whitham modula-
tion theory to obtain an asymptotic analytical description for a full range of the depth
ratio across the bore. The positions of the edges of the undular bore and the amplitude
of the leading solitary wave are found as functions of this depth ratio. The formation
of a partial undular bore with a rapidly-varying finite-amplitude rear wave front is
predicted for depth ratios across the bore exceeding 1.43. The analytical results from
the modulation theory are shown to be in excellent agreement with the full numerical
solution for the development of an undular bore in the Green-Naghdi system.
History
School
- Science
Department
- Mathematical Sciences
Pages
425853 bytesPublication date
2005Notes
This is a pre-print.Language
- en