New graphical tools for studying acoustic ray propagation

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Alternatives to the standard Poincare´ section are proposed to cater for some conditions arising in the study of chaotic ray propagation where the usual method of dimension reduction by the Poincare´ section is inadequate because the driving is notperiodic. There are three alternatives proposed which all use the same surface of intersection, but which differ in their use of the values of the dependent variables at the intersections of the rays with the surface. The new reduction techniques are used to examine ray behaviour in a harmonically perturbed Munk profile which supports raychaos. It is found that all three techniques provide a graphical means of distinguishing between regular and irregular motions, and that the space of the mapping associated with one of the mispartitioned in to non intersecting regular and chaotic regions as with the Poincare´ section. A further model with quasi periodic time dependence of the Hamiltonian is examined, and it turns out that the quasi periodic nature of the motion is revealed as Lissajous curves by one technique.
Original languageEnglish
Pages (from-to)850–860
Number of pages11
JournalJournal of Sound and Vibration
Volume324
Issue number3-5
Early online date14 Mar 2009
DOIs
Publication statusPublished - Jul 2009

Fingerprint

geometrical acoustics
rays
Acoustics
Hamiltonians
intersections
propagation
dependent variables
time dependence
curves
profiles

Cite this

New graphical tools for studying acoustic ray propagation. / Bodai, Tamas; Fenwick, Alan J.; Wiercigroch, Marian.

In: Journal of Sound and Vibration, Vol. 324, No. 3-5, 07.2009, p. 850–860.

Research output: Contribution to journalArticle

@article{6dacc3d49a0b498ca18413e2ccb379b8,
title = "New graphical tools for studying acoustic ray propagation",
abstract = "Alternatives to the standard Poincare´ section are proposed to cater for some conditions arising in the study of chaotic ray propagation where the usual method of dimension reduction by the Poincare´ section is inadequate because the driving is notperiodic. There are three alternatives proposed which all use the same surface of intersection, but which differ in their use of the values of the dependent variables at the intersections of the rays with the surface. The new reduction techniques are used to examine ray behaviour in a harmonically perturbed Munk profile which supports raychaos. It is found that all three techniques provide a graphical means of distinguishing between regular and irregular motions, and that the space of the mapping associated with one of the mispartitioned in to non intersecting regular and chaotic regions as with the Poincare´ section. A further model with quasi periodic time dependence of the Hamiltonian is examined, and it turns out that the quasi periodic nature of the motion is revealed as Lissajous curves by one technique.",
author = "Tamas Bodai and Fenwick, {Alan J.} and Marian Wiercigroch",
year = "2009",
month = "7",
doi = "10.1016/j.jsv.2009.01.049",
language = "English",
volume = "324",
pages = "850–860",
journal = "Journal of Sound and Vibration",
issn = "0022-460X",
publisher = "Academic Press Inc.",
number = "3-5",

}

TY - JOUR

T1 - New graphical tools for studying acoustic ray propagation

AU - Bodai, Tamas

AU - Fenwick, Alan J.

AU - Wiercigroch, Marian

PY - 2009/7

Y1 - 2009/7

N2 - Alternatives to the standard Poincare´ section are proposed to cater for some conditions arising in the study of chaotic ray propagation where the usual method of dimension reduction by the Poincare´ section is inadequate because the driving is notperiodic. There are three alternatives proposed which all use the same surface of intersection, but which differ in their use of the values of the dependent variables at the intersections of the rays with the surface. The new reduction techniques are used to examine ray behaviour in a harmonically perturbed Munk profile which supports raychaos. It is found that all three techniques provide a graphical means of distinguishing between regular and irregular motions, and that the space of the mapping associated with one of the mispartitioned in to non intersecting regular and chaotic regions as with the Poincare´ section. A further model with quasi periodic time dependence of the Hamiltonian is examined, and it turns out that the quasi periodic nature of the motion is revealed as Lissajous curves by one technique.

AB - Alternatives to the standard Poincare´ section are proposed to cater for some conditions arising in the study of chaotic ray propagation where the usual method of dimension reduction by the Poincare´ section is inadequate because the driving is notperiodic. There are three alternatives proposed which all use the same surface of intersection, but which differ in their use of the values of the dependent variables at the intersections of the rays with the surface. The new reduction techniques are used to examine ray behaviour in a harmonically perturbed Munk profile which supports raychaos. It is found that all three techniques provide a graphical means of distinguishing between regular and irregular motions, and that the space of the mapping associated with one of the mispartitioned in to non intersecting regular and chaotic regions as with the Poincare´ section. A further model with quasi periodic time dependence of the Hamiltonian is examined, and it turns out that the quasi periodic nature of the motion is revealed as Lissajous curves by one technique.

U2 - 10.1016/j.jsv.2009.01.049

DO - 10.1016/j.jsv.2009.01.049

M3 - Article

VL - 324

SP - 850

EP - 860

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

SN - 0022-460X

IS - 3-5

ER -