Particle Trajectories in Nonlinear Schrödinger Models

Carter, John D.; Curtis, Christopher W.; Kalisch, Henrik

doi:10.1007/s42286-019-00008-7

Cited by 18 publications

(12 citation statements)

References 33 publications

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“…After calculating the numerical solution of the wind forced NLS (12), the corresponding sea surface displacement can be determined by equation (9). For the computation of the wave kinematics, particle trajectories and hydrodynamic forces acting on a mechanical structure, the velocity potential f has to be computed.…”

Section: Computation Of Particle Trajectories and Hydrodynamic Forcesmentioning

confidence: 99%

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Determination of particle paths and hydrodynamic forces of random wind forced nonlinear ocean waves

Hollm,

Dostal,

Carter

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part M:

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The hydrodynamic forces of nonlinear deep water gravity waves acting on cylindrical offshore structures are studied. Thereby, the waves are excited by random wind and the corresponding effect on the particle paths and hydrodynamic forces is investigated. This is done for the Peregrine breather solution of the nonlinear Schrödinger equation, which is nowadays considered as a prototype of extreme waves in open seas. Using this theory, the loads on mechanical structures can be calculated efficiently. It is shown that the Peregrine breather can exist under strong and gusty wind conditions and the water particles experience a horizontal drift. This leads to a force with randomly increasing amplitude in time, whereby a mean wind velocity of 50 km/h results in an increase of about 3%. The increase of hydrodynamic forces caused by the wind should therefore be considered for the construction of mechanical structures operating in the ocean.

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Section: Computation Of Particle Trajectories and Hydrodynamic Forcesmentioning

confidence: 99%

“…For this, the velocity potential corresponding to the water waves has to be computed. Carter et al 9 have shown how the velocity potential can be calculated if the wave envelope of the solution of the NLS is known.…”

Section: Introductionmentioning

confidence: 99%

Determination of particle paths and hydrodynamic forces of random wind forced nonlinear ocean waves

Hollm,

Dostal,

Carter

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part M:

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“…We will proceed using Korteweg-de Vries Benjamin-Ono equation to approximate the velocity field in the bulk of the fluid and then extract information about the flow structure beneath the wave. This methodology of approximating the velocity field through reduced models has been adopted in other studies such as in irrotational gravity flows [7,8,9], in gravity flows with constant vorticity [10,11,12,13], in capillary-gravity flows with constant vorticity [14,15] and in gravity flows with variable vorticity [16]. There is no doubt that solving the full Euler equations provides a more complete description of the flow.…”

Section: Introductionmentioning

confidence: 99%

An investigation of the flow structure beneath solitary waves with constant vorticity on a conducting fluid under normal electric fields

Flamarion¹,

Gao²,

Ribeiro-Jr³

2023

Preprint

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The motion of an interface separating two fluids under the effect of electric fields is a subject that has picked the attention of researchers from different areas. While there is an abundance of studies investigating the free surface wave properties, very few works have examined the associated velocity field within the bulk of the fluid. Therefore, in this paper, we investigate numerically the flow structure beneath solitary waves with constant vorticity on an inviscid conducting fluid bounded above by a dielectric gas under normal electric fields in the framework of a weakly nonlinear theory. Elevation and depression solitary waves with constant vorticity are computed by a pseudo-spectral method and a parameter sweep on the intensity of the electric field is carried out in order to study its role in the appearance of stagnation points. We find that for elevation solitary waves the location of stagnation points does not change significantly with variations of the electric field. For depression solitary waves, on the other hand, the electric field acts as a catalyser that makes possible the appearance of stagnation points -in the sense that in its absence there is no stagnation point.

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“…We will proceed with using reduced models to approximate the velocity field in the bulk of the fluid and then extract information about the flow structure beneath the wave. Such methodology has been adopted in other works such as irrotational gravity flows in [25,26,27], gravity flows with constant vorticity in [14,28,29,30], capillary-gravity flows with constant vorticity in [31,32] and gravity flows with variable vorticity in [33]. There is no doubt that solving the full Euler equations provides a more complete description of the flow.…”

Section: Introductionmentioning

confidence: 99%

An investigation of the flow structure beneath solitary waves with constant vorticity on a conducting fluid under normal electric fields

2023

View full text Add to dashboard Cite

The motion of an interface separating two fluids under the effect of electric fields is a subject that has picked the attention of researchers from different areas. While there is an abundance of studies investigating the free surface wave properties, very few works have examined the associated velocity field within the bulk of the fluid. Therefore, in this paper, we investigate numerically the flow structure beneath solitary waves with constant vorticity on an inviscid conducting fluid bounded above by a dielectric gas under normal electric fields in the framework of a weakly nonlinear theory. Elevation and depression solitary waves with constant vorticity are computed by a pseudo-spectral method and a parameter sweep on the intensity of the electric field is carried out in order to study its role in the appearance of stagnation points. We find that for elevation solitary waves the location of stagnation points does not change significantly with variations of the electric field. For depression solitary waves, on the other hand, the electric field acts as a catalyser that makes possible the appearance of stagnation points - in the sense that in its absence there is no stagnation point.

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Particle Trajectories in Nonlinear Schrödinger Models

Cited by 18 publications

References 33 publications

Determination of particle paths and hydrodynamic forces of random wind forced nonlinear ocean waves

Determination of particle paths and hydrodynamic forces of random wind forced nonlinear ocean waves

An investigation of the flow structure beneath solitary waves with constant vorticity on a conducting fluid under normal electric fields

An investigation of the flow structure beneath solitary waves with constant vorticity on a conducting fluid under normal electric fields

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