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Solitary waves in forked channel regions

Published online by Cambridge University Press:  20 July 2015

A. Nachbin  and
V. S. Simões
A. Nachbin*
Affiliation:
Instituto Nacional de Matemática Pura e Aplicada, Estrada D. Castorina, 110, Rio de Janeiro, RJ, CEP 22460-320, Brazil
V. S. Simões
Affiliation:
Instituto Nacional de Matemática Pura e Aplicada, Estrada D. Castorina, 110, Rio de Janeiro, RJ, CEP 22460-320, Brazil
*
†Email address for correspondence: nachbin@impa.br
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Abstract

Solitary water waves travelling through a forked channel region are studied via a new nonlinear wave model. This novel (reduced) one-dimensional (1D) model captures the effective features of the reflection and transmission of solitary waves passing through a two-dimensional (2D) branching channel region. Using an appropriate change of coordinates, the 2D wave system is defined in a simpler geometric configuration that allows a straightforward reduction to a 1D graph-like configuration. The Jacobian of the change of coordinates leads to a variable coefficient in the 1D model, which contains information about the angles of the diverting reaches, a feature that is not present in any previous water wave model on networks. Furthermore, this new formulation is more general, in allowing both symmetric and asymmetric branching configurations to be considered. A new compatibility condition is deduced, which is used at the corresponding branching node. The 2D and 1D dynamics are compared, with very good agreement.

JFM classification

Waves/Free-surface Flows: Channel flow Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 777 , 25 August 2015 , pp. 544 - 568
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Copyright
© 2015 Cambridge University Press 

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