Dynamical time scales generated by a model nonlinear Hamiltonian

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Zakharov and L'vov long ago invoked a Kolmogorov cascade hypothesis to describe the modal transfer of energy for surface gravity waves in deep water. Within this context the cascade hypothesis requires the existence of dynamical time scales in the evolution of the mode amplitudes which scale with wave number. The purpose of this Letter is to study the temporal evolution of individual modes, with the aim of identifying these dynamical time scales. The main result reported here is that mode-dependent time scales τ(k)∼k-β can indeed be identified, with exponent β related to the exponent α which describes the spectrum of the waveheight autocorrelation function.

Original languageEnglish (US)
Pages (from-to)1172-1175
Number of pages4
JournalPhysical Review Letters
Volume71
Issue number8
DOIs
StatePublished - Jan 1 1993

Fingerprint

cascades
exponents
deep water
gravity waves
autocorrelation
energy

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Dynamical time scales generated by a model nonlinear Hamiltonian. / Willemsen, Jorge.

In: Physical Review Letters, Vol. 71, No. 8, 01.01.1993, p. 1172-1175.

Research output: Contribution to journalArticle

@article{bd4f2067f19f4b93ad038aae5c3be43a,
title = "Dynamical time scales generated by a model nonlinear Hamiltonian",
abstract = "Zakharov and L'vov long ago invoked a Kolmogorov cascade hypothesis to describe the modal transfer of energy for surface gravity waves in deep water. Within this context the cascade hypothesis requires the existence of dynamical time scales in the evolution of the mode amplitudes which scale with wave number. The purpose of this Letter is to study the temporal evolution of individual modes, with the aim of identifying these dynamical time scales. The main result reported here is that mode-dependent time scales τ(k)∼k-β can indeed be identified, with exponent β related to the exponent α which describes the spectrum of the waveheight autocorrelation function.",
author = "Jorge Willemsen",
year = "1993",
month = "1",
day = "1",
doi = "10.1103/PhysRevLett.71.1172",
language = "English (US)",
volume = "71",
pages = "1172--1175",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "8",

}

TY - JOUR

T1 - Dynamical time scales generated by a model nonlinear Hamiltonian

AU - Willemsen, Jorge

PY - 1993/1/1

Y1 - 1993/1/1

N2 - Zakharov and L'vov long ago invoked a Kolmogorov cascade hypothesis to describe the modal transfer of energy for surface gravity waves in deep water. Within this context the cascade hypothesis requires the existence of dynamical time scales in the evolution of the mode amplitudes which scale with wave number. The purpose of this Letter is to study the temporal evolution of individual modes, with the aim of identifying these dynamical time scales. The main result reported here is that mode-dependent time scales τ(k)∼k-β can indeed be identified, with exponent β related to the exponent α which describes the spectrum of the waveheight autocorrelation function.

AB - Zakharov and L'vov long ago invoked a Kolmogorov cascade hypothesis to describe the modal transfer of energy for surface gravity waves in deep water. Within this context the cascade hypothesis requires the existence of dynamical time scales in the evolution of the mode amplitudes which scale with wave number. The purpose of this Letter is to study the temporal evolution of individual modes, with the aim of identifying these dynamical time scales. The main result reported here is that mode-dependent time scales τ(k)∼k-β can indeed be identified, with exponent β related to the exponent α which describes the spectrum of the waveheight autocorrelation function.

UR - http://www.scopus.com/inward/record.url?scp=3042512421&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042512421&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.71.1172

DO - 10.1103/PhysRevLett.71.1172

M3 - Article

AN - SCOPUS:3042512421

VL - 71

SP - 1172

EP - 1175

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 8

ER -