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

Brink, Jeandrew; Teukolsky, Saul A; Wasserman, Ira

doi:10.1103/PhysRevD.70.121501

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

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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{sup -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{sup 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 ofmore »« less

Authors:

Brink, Jeandrew; Teukolsky, Saul A; Wasserman, Ira ^[1]

Center for Radiophysics and Space Research, Cornell University, Ithaca New York 14853 (United States)

Publication Date:: Wed Dec 15 00:00:00 EST 2004

OSTI Identifier:: 20698197

Resource Type:: Journal Article

Journal Name:: Physical Review. D, Particles Fields

Additional Journal Information:: Journal Volume: 70; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.70.121501; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; COMPUTERIZED SIMULATION; COUPLING; DAMPING; ENERGY TRANSFER; GRAVITATION; GRAVITATIONAL WAVES; NEUTRON STARS; NONLINEAR PROBLEMS; OSCILLATORS; PARAMETRIC INSTABILITIES

Citation Formats


                    Brink, Jeandrew, Teukolsky, Saul A, Wasserman, Ira, Center for Radiophysics and Space Research, Cornell University, Ithaca New York 14853, and Center for Radiophysics and Space Research, Cornell University, Ithaca New York 14853. Nonlinear couplings of R-modes: Energy transfer and saturation amplitudes at realistic timescales.  United States: N. p., 2004. 
        Web.  doi:10.1103/PhysRevD.70.121501.

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                    Brink, Jeandrew, Teukolsky, Saul A, Wasserman, Ira, Center for Radiophysics and Space Research, Cornell University, Ithaca New York 14853, & Center for Radiophysics and Space Research, Cornell University, Ithaca New York 14853. Nonlinear couplings of R-modes: Energy transfer and saturation amplitudes at realistic timescales.  United States.  https://doi.org/10.1103/PhysRevD.70.121501

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                    Brink, Jeandrew, Teukolsky, Saul A, Wasserman, Ira, Center for Radiophysics and Space Research, Cornell University, Ithaca New York 14853, and Center for Radiophysics and Space Research, Cornell University, Ithaca New York 14853. 2004.  
        "Nonlinear couplings of R-modes: Energy transfer and saturation amplitudes at realistic timescales".  United States.  https://doi.org/10.1103/PhysRevD.70.121501.

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@article{osti_20698197,

  title        = {Nonlinear couplings of R-modes: Energy transfer and saturation amplitudes at realistic timescales},

  author       = {Brink, Jeandrew and Teukolsky, Saul A and Wasserman, Ira and Center for Radiophysics and Space Research, Cornell University, Ithaca New York 14853 and Center for Radiophysics and Space Research, Cornell University, Ithaca New York 14853},

  abstractNote = {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{sup -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{sup 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.},

  doi          = {10.1103/PhysRevD.70.121501},

  url          = {https://www.osti.gov/biblio/20698197},
  journal      = {Physical Review. D, Particles Fields},

  issn         = {0556-2821},

  number       = 12,

  volume       = 70,

  place        = {United States},

  year         = {Wed Dec 15 00:00:00 EST 2004},

  month        = {Wed Dec 15 00:00:00 EST 2004}

}

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