Particle trajectories in extreme stokes waves over infinite depth

Tony Lyons

doi:10.3934/dcds.2014.34.3095

Particle trajectories in extreme stokes waves over infinite depth

Tony Lyons

Research output: Contribution to journal › Article › peer-review

27 Citations (Scopus)

Abstract

We investigate the velocity field of fluid particles in an extreme water wave over infinite depth. It is shown that the trajectories of particles within the fluid and along the free surface do not form closed paths over the course of one period, but rather undergo a positive drift in the direction of wave propagation. In addition it is shown that the wave crest cannot form a stagnation point despite the velocity of the fluid particles being zero there.

Original language	English
Pages (from-to)	3095-3107
Number of pages	13
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	34
Issue number	8
DOIs	https://doi.org/10.3934/dcds.2014.34.3095
Publication status	Published - Aug 2014
Externally published	Yes

Keywords

Maximum principles
Particle trajectory
Stokes wave
Weak solution

Access to Document

10.3934/dcds.2014.34.3095

Cite this

@article{ab54405bba6948cc8b1b44b1c5a7a868,

title = "Particle trajectories in extreme stokes waves over infinite depth",

abstract = "We investigate the velocity field of fluid particles in an extreme water wave over infinite depth. It is shown that the trajectories of particles within the fluid and along the free surface do not form closed paths over the course of one period, but rather undergo a positive drift in the direction of wave propagation. In addition it is shown that the wave crest cannot form a stagnation point despite the velocity of the fluid particles being zero there.",

keywords = "Maximum principles, Particle trajectory, Stokes wave, Weak solution",

author = "Tony Lyons",

year = "2014",

month = aug,

doi = "10.3934/dcds.2014.34.3095",

language = "English",

volume = "34",

pages = "3095--3107",

journal = "Discrete and Continuous Dynamical Systems- Series A",

issn = "1078-0947",

publisher = "American Institute of Mathematical Sciences",

number = "8",

}

TY - JOUR

T1 - Particle trajectories in extreme stokes waves over infinite depth

AU - Lyons, Tony

PY - 2014/8

Y1 - 2014/8

N2 - We investigate the velocity field of fluid particles in an extreme water wave over infinite depth. It is shown that the trajectories of particles within the fluid and along the free surface do not form closed paths over the course of one period, but rather undergo a positive drift in the direction of wave propagation. In addition it is shown that the wave crest cannot form a stagnation point despite the velocity of the fluid particles being zero there.

AB - We investigate the velocity field of fluid particles in an extreme water wave over infinite depth. It is shown that the trajectories of particles within the fluid and along the free surface do not form closed paths over the course of one period, but rather undergo a positive drift in the direction of wave propagation. In addition it is shown that the wave crest cannot form a stagnation point despite the velocity of the fluid particles being zero there.

KW - Maximum principles

KW - Particle trajectory

KW - Stokes wave

KW - Weak solution

UR - http://www.scopus.com/inward/record.url?scp=84893300928&partnerID=8YFLogxK

U2 - 10.3934/dcds.2014.34.3095

DO - 10.3934/dcds.2014.34.3095

M3 - Article

AN - SCOPUS:84893300928

VL - 34

SP - 3095

EP - 3107

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

SN - 1078-0947

IS - 8

ER -

Particle trajectories in extreme stokes waves over infinite depth

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this