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Mode Coupling: Quadratic Perturbation Scheme

  • Pantelis PnigourasEmail author
Chapter
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Part of the Springer Theses book series (Springer Theses)

Abstract

The process we will follow is similar to that of Chap.  2 for linear perturbations, but now we are also going to consider quadratic terms to define the perturbations (Sect. 4.1). We will show that, in the quadratic-perturbation approximation, modes couple in triplets, which satisfy a resonance condition (Sect. 4.2). Coupling of an unstable mode to other (stable) modes of the star can lead to the saturation of the unstable mode’s amplitude, through a mechanism known as parametric resonance instability (Sect. 4.3). For the saturation to be successful, some stability conditions, which determine the amplitude evolution of the coupled triplet, have to be satisfied (Sect. 4.4), with some interesting behaviours occurring throughout the parameter space, like limit cycles, chaotic orbits, and frequency synchronisation.

Keywords

Quadratic Perturbation Parametric Resonance Instability Triplet Coupling Amplitude Evolution Unstable Modes 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Mathematical Sciences and STAG Research CentreUniversity of SouthamptonSouthamptonUK

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