A boundary integral formulation for particle trajectories  in Stokes waves

Nachbin, André; Ribeiro-Junior, R.

doi:10.3934/dcds.2014.34.3135

Cited by 25 publications

(22 citation statements)

References 20 publications

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“…Water flows with a uniform underlying current (possibly absent) are termed irrotational flows, while rotational waves describe the interaction of surface water waves with non-uniform currents. The study of the flow beneath an irrotational two-dimensional surface wave in water with a flat bed is quite well-understood: see [3,7] for theoretical studies, [2,12] for numerical simulations and [1,14] for experimental data. For rotational two-dimensional travelling water waves an existence theory for waves of large amplitude is available [6] and some numerical simulations were performed in the case of constant vorticity flows without stagnation points [10,11] and in the presence of stagnation points [13].…”

Section: Introductionmentioning

confidence: 99%

A Penalization Method for Calculating the Flow Beneath Traveling Water Waves of Large Amplitude

Constantin¹,

Kalimeris²,

Scherzer³

2015

SIAM J. Appl. Math.

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Section: Introductionmentioning

confidence: 99%

A Penalization Method for Calculating the Flow Beneath Traveling Water Waves of Large Amplitude

Constantin¹,

Kalimeris²,

Scherzer³

2015

SIAM J. Appl. Math.

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“…Therefore, in the presence of a uniform counter-current, it is always possible to find closed orbits (Constantin & Strauss 2010). Nachbin & Ribeiro Jr (2014) observed this fact numerically with an accurate boundary integral method. A common model for waves in rotational flow is the case of constant vorticity.…”

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confidence: 97%

Flow structure beneath rotational water waves with stagnation points

Ribeiro

Milewski²,

Nachbin

2017

J. Fluid Mech.

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The purpose of this work is to explore in detail the structure of the interior flow generated by periodic surface waves on a fluid with constant vorticity. The problem is mapped conformally to a strip and solved numerically using spectral methods. Once the solution is known, the streamlines, pressure and particle paths can be found and mapped back to the physical domain. We find that the flow beneath the waves contains zero, one, two or three stagnation points in a frame moving with the wave speed, and describe the bifurcations between these flows. When the vorticity is sufficiently strong, the pressure in the flow and on the bottom boundary also has very different features from the usual irrotational wave case.

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“…We now summarize our particle trajectories algorithm [1] based on the boundary integral formulation. We recall that the travelling wave profile does not depend on the value of the current.…”

Section: Boundary Integral Formulation Of Irrotational Wavesmentioning

confidence: 99%

Capturing the flow beneath water waves

Nachbin

Ribeiro-Junior

2017

Phil. Trans. R. Soc. A.

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Recently, the authors presented two numerical studies for capturing the flow structure beneath water waves (Nachbin and Ribeiro-Junior 2014 , 3135-3153 (doi:10.3934/dcds.2014.34.3135); Ribeiro-Junior 2017 , 792-814 (doi:10.1017/jfm.2016.820)). Closed orbits for irrotational waves with an opposing current and stagnation points for rotational waves were some of the issues addressed. This paper summarizes the numerical strategies adopted for capturing the flow beneath irrotational and rotational water waves. It also presents new preliminary results for particle trajectories, due to irrotational waves, in the presence of a bottom topography.This article is part of the theme issue 'Nonlinear water waves'.

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A boundary integral formulation for particle trajectories in Stokes waves

Cited by 25 publications

References 20 publications

A Penalization Method for Calculating the Flow Beneath Traveling Water Waves of Large Amplitude

A Penalization Method for Calculating the Flow Beneath Traveling Water Waves of Large Amplitude

Flow structure beneath rotational water waves with stagnation points

Capturing the flow beneath water waves

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