The modulation instability revisited

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The modulational instability (or "Benjamin-Feir instability") has been a fundamental principle of nonlinear wave propagation in systems without dissipation ever since it was discovered in the 1960s. It is often identified as a mechanism by which energy spreads from one dominant Fourier mode to neighboring modes. In recent work, we have explored how damping affects this instability, both mathematically and experimentally. Mathematically, the modulational instability changes fundamentally in the presence of damping: for waves of small or moderate amplitude, damping (of the right kind) stabilizes the instability. Experimentally, we observe wavetrains of small or moderate amplitude that are stable within the lengths of our wavetanks, and we find that the damped theory predicts the evolution of these wavetrains much more accurately than earlier theories. For waves of larger amplitude, neither the standard (undamped) theory nor the damped theory is accurate, because frequency down shifting affects the evolution in ways that are still poorly understood.

Original languageEnglish (US)
Pages (from-to)25-43
Number of pages19
JournalEuropean Physical Journal: Special Topics
Volume147
Issue number1
DOIs
StatePublished - Aug 1 2007

Fingerprint

Modulation
modulation
Damping
damping
Wave propagation
wave propagation
dissipation
energy

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

@article{b728302ed1764951965fdc5b8a26807f,
title = "The modulation instability revisited",
abstract = "The modulational instability (or {"}Benjamin-Feir instability{"}) has been a fundamental principle of nonlinear wave propagation in systems without dissipation ever since it was discovered in the 1960s. It is often identified as a mechanism by which energy spreads from one dominant Fourier mode to neighboring modes. In recent work, we have explored how damping affects this instability, both mathematically and experimentally. Mathematically, the modulational instability changes fundamentally in the presence of damping: for waves of small or moderate amplitude, damping (of the right kind) stabilizes the instability. Experimentally, we observe wavetrains of small or moderate amplitude that are stable within the lengths of our wavetanks, and we find that the damped theory predicts the evolution of these wavetrains much more accurately than earlier theories. For waves of larger amplitude, neither the standard (undamped) theory nor the damped theory is accurate, because frequency down shifting affects the evolution in ways that are still poorly understood.",
author = "H. Segur and Henderson, {Diane Marie}",
year = "2007",
month = "8",
day = "1",
doi = "10.1140/epjst/e2007-00201-1",
language = "English (US)",
volume = "147",
pages = "25--43",
journal = "European Physical Journal: Special Topics",
issn = "1951-6355",
publisher = "Springer Verlag",
number = "1",

}

The modulation instability revisited. / Segur, H.; Henderson, Diane Marie.

In: European Physical Journal: Special Topics, Vol. 147, No. 1, 01.08.2007, p. 25-43.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The modulation instability revisited

AU - Segur, H.

AU - Henderson, Diane Marie

PY - 2007/8/1

Y1 - 2007/8/1

N2 - The modulational instability (or "Benjamin-Feir instability") has been a fundamental principle of nonlinear wave propagation in systems without dissipation ever since it was discovered in the 1960s. It is often identified as a mechanism by which energy spreads from one dominant Fourier mode to neighboring modes. In recent work, we have explored how damping affects this instability, both mathematically and experimentally. Mathematically, the modulational instability changes fundamentally in the presence of damping: for waves of small or moderate amplitude, damping (of the right kind) stabilizes the instability. Experimentally, we observe wavetrains of small or moderate amplitude that are stable within the lengths of our wavetanks, and we find that the damped theory predicts the evolution of these wavetrains much more accurately than earlier theories. For waves of larger amplitude, neither the standard (undamped) theory nor the damped theory is accurate, because frequency down shifting affects the evolution in ways that are still poorly understood.

AB - The modulational instability (or "Benjamin-Feir instability") has been a fundamental principle of nonlinear wave propagation in systems without dissipation ever since it was discovered in the 1960s. It is often identified as a mechanism by which energy spreads from one dominant Fourier mode to neighboring modes. In recent work, we have explored how damping affects this instability, both mathematically and experimentally. Mathematically, the modulational instability changes fundamentally in the presence of damping: for waves of small or moderate amplitude, damping (of the right kind) stabilizes the instability. Experimentally, we observe wavetrains of small or moderate amplitude that are stable within the lengths of our wavetanks, and we find that the damped theory predicts the evolution of these wavetrains much more accurately than earlier theories. For waves of larger amplitude, neither the standard (undamped) theory nor the damped theory is accurate, because frequency down shifting affects the evolution in ways that are still poorly understood.

UR - http://www.scopus.com/inward/record.url?scp=34548363440&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548363440&partnerID=8YFLogxK

U2 - 10.1140/epjst/e2007-00201-1

DO - 10.1140/epjst/e2007-00201-1

M3 - Article

AN - SCOPUS:34548363440

VL - 147

SP - 25

EP - 43

JO - European Physical Journal: Special Topics

JF - European Physical Journal: Special Topics

SN - 1951-6355

IS - 1

ER -