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The oscillation and stability of differentially rotating spherical shells

The oscillation and stability of differentially rotating spherical shells
The oscillation and stability of differentially rotating spherical shells
An understanding of the oscillations of differentially rotating systems is key to many areas of astrophysics. It is of particular relevance to the emission of gravitational waves from oscillating neutron stars, which are expected to possess significant differential rotation immediately after birth or binary merger. In a previous paper we analysed the normal modes of a simple system exhibiting differential rotation. In this complementary paper we address the initial-value problem for the same simple model using both analytical methods and numerical time-evolutions. We derive a necessary and sufficient condition for dynamical shear instability. We discuss the dynamical behaviour of the continuous spectrum in response to an initial perturbation, and show that certain singular solutions within the continuous spectrum appear physically indistinguishable from the discrete modes outside the continuous spectrum.
0035-8711
927
Watts, Anna L.
8c906b14-9fb9-4f04-9cb3-2aabd6561162
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Williams, R.L.
ddbad5c7-b3bd-41d8-a79b-6092e7c41136
Watts, Anna L.
8c906b14-9fb9-4f04-9cb3-2aabd6561162
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Williams, R.L.
ddbad5c7-b3bd-41d8-a79b-6092e7c41136

Watts, Anna L., Andersson, Nils and Williams, R.L. (2004) The oscillation and stability of differentially rotating spherical shells. Monthly Notices of the Royal Astronomical Society, 350 (3), 927. (doi:10.1111/j.1365-2966.2004.07695.x).

Record type: Article

Abstract

An understanding of the oscillations of differentially rotating systems is key to many areas of astrophysics. It is of particular relevance to the emission of gravitational waves from oscillating neutron stars, which are expected to possess significant differential rotation immediately after birth or binary merger. In a previous paper we analysed the normal modes of a simple system exhibiting differential rotation. In this complementary paper we address the initial-value problem for the same simple model using both analytical methods and numerical time-evolutions. We derive a necessary and sufficient condition for dynamical shear instability. We discuss the dynamical behaviour of the continuous spectrum in response to an initial perturbation, and show that certain singular solutions within the continuous spectrum appear physically indistinguishable from the discrete modes outside the continuous spectrum.

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Published date: 2004

Identifiers

Local EPrints ID: 29459
URI: http://eprints.soton.ac.uk/id/eprint/29459
ISSN: 0035-8711
PURE UUID: 28fb663a-e11e-4857-8ba0-ea339f55d7ad
ORCID for Nils Andersson: ORCID iD orcid.org/0000-0001-8550-3843

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Date deposited: 12 May 2006
Last modified: 28 Apr 2022 01:43

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Contributors

Author: Anna L. Watts
Author: Nils Andersson ORCID iD
Author: R.L. Williams

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