Internal flow properties in a capillary bore

Wong, Wei-Ying; Bjørnestad, Maria; Lin, Chang; Kao, Ming-Jer; Kalisch, Henrik; Guyenne, Philippe; Roeber, Volker; Yuan, Juan-Ming

doi:10.1063/1.5124038

Cited by 8 publications

(7 citation statements)

References 52 publications

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“…In particular, it is of interest to examine the precise role of dispersive dynamics vis-à-vis the regions dominated by hyperbolic regimes such as the "shoulders" we have identified in Section 2.1. In particular, the transition between hyperbolic and dispersive dominated dynamics, which can be expected to occur when the typical Froude number of the flow |u|/ g|η| nears unity (see, e.g., [32]), would modify the shoulders' generation and evolution, which could require developing an intermediate model to study. Further extension to stratified systems with two or more layers of different densities is also of interest, and in the special case of two-layer fluids in Boussinesq approximation our results can be applied almost directly thanks to the map to the shallow water system (paying attention to the additional subtleties caused by the map's multivaluedness) [10,22].…”

Section: Discussionmentioning

confidence: 99%

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Evolution of interface singularities in shallow water equations with variable bottom topography

Camassa¹,

R.²,

Falqui³

et al. 2022

Preprint

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Wave front propagation with non-trivial bottom topography is studied within the formalism of hyperbolic long wave models. Evolution of non-smooth initial data is examined, and in particular the splitting of singular points and their short time behaviour is described. In the opposite limit of longer times, the local analysis of wavefronts is used to estimate the gradient catastrophe formation and how this is influenced by the topography. The limiting cases when the free surface intersects the bottom boundary, belonging to the so-called "physical" and "non-physical" vacuum classes, are examined. Solutions expressed by power series in the spatial variable lead to a hierarchy of ordinary differential equations for the time-dependent series coefficients, which are shown to reveal basic differences between the two vacuum cases: for non-physical vacuums, the equations of the hierarchy are recursive and linear past the first two pairs, while for physical vacuums the hierarchy is non-recursive, fully coupled and nonlinear. The former case may admit solutions that are free of singularities for nonzero time intervals, while the latter is shown to develop non-standard velocity shocks instantaneously. Polynomial bottom topographies simplify the hierarchy, as they contribute only a finite number of inhomogeneous forcing terms to the equations in the recursion relations. However, we show that truncation to finite dimensional systems and polynomial solutions is in general only possible for the case of a quadratic bottom profile. In this case the system's evolution can reduce to, and is completely described by, a low dimensional dynamical system for the time-dependent coefficients. This system encapsulates all the nonlinear properties of the solution for general power series initial data, and in particular governs the loss of regularity in finite times at the dry point. For the special case of parabolic bottom topographies, an exact, self-similar solution class is introduced and studied to illustrate via closed form expressions the general results. IntroductionBottom topography, and, in general, sloped boundaries add a layer of difficulty to the study of the hydrodynamics of water waves, and as such have been a classical subject of the literature, stemming 1

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Section: Discussionmentioning

confidence: 99%

“…We thank the anonymous referees for useful suggestions on the paper's exposition and for alerting us to references [30,25,32]. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant no 778010 IPaDEGAN.…”

Section: Acknowledgementsmentioning

confidence: 99%

Evolution of interface singularities in shallow water equations with variable bottom topography

Camassa¹,

R.²,

Falqui³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…In particular, the transition between hyperbolic and dispersive dominated dynamics, which can be expected to occur when the typical Froude number of the flow

|u|/\sqrt {g |\eta |}

nears unity (see, e.g., Ref. 24), would modify the shoulders' generation and evolution, which could require developing an intermediate model for such a study. Further extension to stratified systems with two or more layers of different densities is also of interest, and in the special case of two‐layer fluids in Boussinesq approximation our results can be applied almost directly, thanks to the map to the shallow water system (paying attention to the additional subtleties caused by the map's multivaluedness) 16,25 …”

Section: Discussionmentioning

confidence: 99%

“…We thank the anonymous referees for useful suggestions on the paper's exposition and for alerting us to references. 17,21,24 This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant no 778010 IPaDEGAN. We also gratefully acknowledge the auspices of the GNFM Section of INdAM under which part of this work was carried out.…”

Section: A C K N O W L E D G M E N T Smentioning

confidence: 99%

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Evolution of interface singularities in shallow water equations with variable bottom topography

Camassa

Falqui

et al. 2022

Stud Appl Math

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Wave front propagation with nontrivial bottom topography is studied within the formalism of hyperbolic long wave models. Evolution of nonsmooth initial data is examined, and, in particular, the splitting of singular points and their short time behavior is described. In the opposite limit of longer times, the local analysis of wave fronts is used to estimate the gradient catastrophe formation and how this is influenced by the topography. The limiting cases when the free surface intersects the bottom boundary, belonging to the so-called "physical" and "nonphysical" vacuum classes, are examined.Solutions expressed by power series in the spatial variable lead to a hierarchy of ordinary differential equations for the time-dependent series coefficients, which are shown to reveal basic differences between the two vacuum cases: for nonphysical vacuums, the equations of the hierarchy are recursive and linear past the first two pairs, whereas for physical vacuums, the hierarchy is nonrecursive, fully coupled, and nonlinear. The former case may admit solutions that are free of singularitiesThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Sudden wave flooding on steep rock shores: a clear but hidden danger

Kalisch,

Lagona,

Roeber

2023

Nat Hazards

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It is shown that very steep coastal profiles can give rise to unexpectedly large wave events at the coast. We conduct a statistical analysis of runs from a nearshore Boussinesq-type model to demonstrate that under certain wave conditions, which a casual observer would perceive as calm, the likelihood of large run-up events is uncharacteristically high. The data computed by the Boussinesq-type model show that sea states with lower overall wave steepness favor higher run-up. Under these wave conditions, more of the available wave energy reaches the shore, since less wave breaking occurs, which can create a false sense of security for beach-goers.

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Internal flow properties in a capillary bore

Cited by 8 publications

References 52 publications

Evolution of interface singularities in shallow water equations with variable bottom topography

Evolution of interface singularities in shallow water equations with variable bottom topography

Evolution of interface singularities in shallow water equations with variable bottom topography

Sudden wave flooding on steep rock shores: a clear but hidden danger

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