Solitary waves in forked channel regions

Nachbin, André; Simões, V. S.

doi:10.1017/jfm.2015.359

Cited by 9 publications

(8 citation statements)

References 18 publications

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“…Not surprisingly, these conditions are very close to the ones obtained by Nachbin and Simoes [10], except for the Jacobian of the conformal transformation.…”

Section: Discussionsupporting

confidence: 84%

Coupling Conditions for Water Waves at Forks

2019

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We considered the propagation of nonlinear shallow water waves in a narrow channel presenting a fork. We aimed at computing the coupling conditions for a 1D effective model, using 2D simulations and an analysis based on the conservation laws. For small amplitudes, this analysis justifies the well-known Stoker interface conditions, so that the coupling does not depend on the angle of the fork. We also find this in the numerical solution. Large amplitude solutions in a symmetric fork also tend to follow Stoker’s relations, due to the symmetry constraint. For non symmetric forks, 2D effects dominate so that it is necessary to understand the flow inside the fork. However, even then, conservation laws give some insight in the dynamics.

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“…Not surprisingly, these conditions are very close to the ones obtained by Nachbin and Simoes [10], except for the Jacobian of the conformal transformation.…”

Section: Discussionsupporting

confidence: 84%

Coupling Conditions for Water Waves at Forks

2019

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“…Shallow water equations in the context of river flow at forks were considered in [45]. Starting with a two-dimensional Boussinesq model in a forked channels region, a reduced one-dimensional equation on a metric graph was deduced in [97], with suitable boundary conditions at vertex. It was also shown in [97] that the reduced model supports propagation of solitary waves.…”

Section: Other Nonlinear Dispersive Wave Models On Metric Graphsmentioning

confidence: 99%

Standing waves on quantum graphs

Kairzhan,

Noja,

Pelinovsky

2022

Preprint

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“…Figure 1 illustrates how our definition ignores the physically relevant embedding of a network into Euclidean space. Quantifying the effects of edge curvature and angles between edges, perhaps following the "limiting" approach of [26], could make for interesting future work.…”

Section: Formulation Of Gbbmb On a Star Networkmentioning

confidence: 99%

A Mass-Conserving Formulation of the Generalized Benjamin-Bona-Mahony-Burgers Equation on Star Networks

Morgan

2021

Preprint

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The generalized Benjamin-Bona-Mahony-Burgers equation (gBBMB) describes the flow of blood through a long, viscoelastic artery. In this article we introduce a formulation of gBBMB valid on networks with semi-infinite edges joined at a single junction, with the network's edges corresponding to a segment of the arterial tree. To reflect sudden changes in the material properties of blood vessels, the coefficients of gBBMB are allowed to take different values on each edge of the network. Critically, our formulation ensures that the total mass of the solution to gBBMB is constant in time, even in the presence of dissipation. We also establish local-in-time well-posedness of this new formulation for sufficiently regular initial data. Then, we show how energy methods can be used to extend the local solution to a solution valid for all positive times, provided certain constraints are imposed on the parameters of the model PDE and the network. To build intuition for how waves scatter off the central junction of a network with two edges, we demonstrate the results of some numerical simulations.

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Solitary waves in forked channel regions

Cited by 9 publications

References 18 publications

Coupling Conditions for Water Waves at Forks

Coupling Conditions for Water Waves at Forks

Standing waves on quantum graphs

A Mass-Conserving Formulation of the Generalized Benjamin-Bona-Mahony-Burgers Equation on Star Networks

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