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Nonlinear couplings of R-modes: Energy transfer and saturation amplitudes at realistic timescales

Brink, Jeandrew and Teukolsky, Saul A. and Wasserman, Ira (2004) Nonlinear couplings of R-modes: Energy transfer and saturation amplitudes at realistic timescales. Physical Review D, 70 (12). Art. No. 121501. ISSN 2470-0010. doi:10.1103/PhysRevD.70.121501. https://resolver.caltech.edu/CaltechAUTHORS:20180605-144149188

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Abstract

Nonlinear interactions among the inertial modes of a rotating fluid can be described by a network of coupled oscillators. We use such a description for an incompressible fluid to study the development of the r-mode instability of rotating neutron stars. A previous hydrodynamical simulation of the r-mode reported the catastrophic decay of large amplitude r-modes. We explain the dynamics and timescale of this decay analytically by means of a single three mode coupling. We argue that at realistic driving and damping rates such large amplitudes will never actually be reached. By numerically integrating a network of nearly 5000 coupled modes, we find that the linear growth of the r-mode ceases before it reaches an amplitude of around 10^(-4). The lowest parametric instability thresholds for the r-mode are calculated and it is found that the r-mode becomes unstable to modes with 13 < n < 15 if modes up to n = 30 are included. Using the network of coupled oscillators, integration times of 10^6 rotational periods are attainable for realistic values of driving and damping rates. Complicated dynamics of the modal amplitudes are observed. The initial development is governed by the three mode coupling with the lowest parametric instability. Subsequently, a large number of modes are excited, which greatly decreases the linear growth rate of the r-mode.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevD.70.121501DOIArticle
https://arxiv.org/abs/gr-qc/0406085arXivDiscussion Paper
ORCID:
AuthorORCID
Teukolsky, Saul A.0000-0001-9765-4526
Additional Information:© 2004 The American Physical Society. Received 23 June 2004; published 6 December 2004. Thanks are due to Larry Kidder and Harald Pfeiffer for invaluable advice on the numerous technical details required for the development of the codes used. J. B. thanks Alain Cloot and Werner Pesch for many helpful insights about fluids. This research is supported in part by NSF grants AST-0307273, PHY-9900672 and PHY-0312072 at Cornell University.
Funders:
Funding AgencyGrant Number
NSFAST-0307273
NSFPHY-9900672
NSFPHY-0312072
Issue or Number:12
Classification Code:PACS numbers: 04.40.Dg, 04.30.Db, 97.10.Sj, 97.60.Jd
DOI:10.1103/PhysRevD.70.121501
Record Number:CaltechAUTHORS:20180605-144149188
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180605-144149188
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86804
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Jun 2018 21:50
Last Modified:15 Nov 2021 20:42

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