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A flux-conservative formalism for convective and dissipative multi-fluid systems, with application to Newtonian superfluid neutron stars

A flux-conservative formalism for convective and dissipative multi-fluid systems, with application to Newtonian superfluid neutron stars
A flux-conservative formalism for convective and dissipative multi-fluid systems, with application to Newtonian superfluid neutron stars
We develop a flux-conservative formalism for a Newtonian multi-fluid system, including dissipation and entrainment (i.e. allowing the momentum of one fluid to be a linear combination of the velocities of all fluids). Maximum use is made of mass, energy, and linear and angular momentum conservation to specify the equations of motion. Also used extensively are insights gleaned from a convective variational action principle, key being the distinction between each velocity and its canonically conjugate momentum. Dissipation is incorporated to second order in the ``thermodynamic forces'' via the approach pioneered by Onsager.
An immediate goal of the investigation is to understand better the number, and form, of independent dissipation terms required for a consistent set of equations of motion in the multi-fluid context. A significant, but seemingly innocuous detail, is that one must be careful to isolate ``forces'' that can be written as total gradients, otherwise errors can be made in relating the net internal force to the net externally applied force. Our long-range aim is to provide a formalism that can be used to model dynamical multi-fluid systems both perturbatively and via fully nonlinear 3D numerical evolutions. To elucidate the formalism we consider the standard model for a heat-conducting, superfluid neutron star, which is believed to be dominated by superfluid neutrons, superconducting protons, and a highly degenerate, ultra-relativistic gas of normal fluid electrons. We determine that in this case there are, in principle, 19 dissipation coefficients in the final set of equations.
0264-9381
5505-5529
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Comer, G.L.
f2c1746c-8638-4268-94f0-e5d4375f0358
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Comer, G.L.
f2c1746c-8638-4268-94f0-e5d4375f0358

Andersson, Nils and Comer, G.L. (2006) A flux-conservative formalism for convective and dissipative multi-fluid systems, with application to Newtonian superfluid neutron stars. Classical and Quantum Gravity, 23 (18), 5505-5529. (doi:10.1088/0264-9381/23/18/003).

Record type: Article

Abstract

We develop a flux-conservative formalism for a Newtonian multi-fluid system, including dissipation and entrainment (i.e. allowing the momentum of one fluid to be a linear combination of the velocities of all fluids). Maximum use is made of mass, energy, and linear and angular momentum conservation to specify the equations of motion. Also used extensively are insights gleaned from a convective variational action principle, key being the distinction between each velocity and its canonically conjugate momentum. Dissipation is incorporated to second order in the ``thermodynamic forces'' via the approach pioneered by Onsager.
An immediate goal of the investigation is to understand better the number, and form, of independent dissipation terms required for a consistent set of equations of motion in the multi-fluid context. A significant, but seemingly innocuous detail, is that one must be careful to isolate ``forces'' that can be written as total gradients, otherwise errors can be made in relating the net internal force to the net externally applied force. Our long-range aim is to provide a formalism that can be used to model dynamical multi-fluid systems both perturbatively and via fully nonlinear 3D numerical evolutions. To elucidate the formalism we consider the standard model for a heat-conducting, superfluid neutron star, which is believed to be dominated by superfluid neutrons, superconducting protons, and a highly degenerate, ultra-relativistic gas of normal fluid electrons. We determine that in this case there are, in principle, 19 dissipation coefficients in the final set of equations.

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More information

Published date: 21 September 2006

Identifiers

Local EPrints ID: 29466
URI: http://eprints.soton.ac.uk/id/eprint/29466
ISSN: 0264-9381
PURE UUID: 6540c2e0-02b8-4f4c-a7f6-895e23204876
ORCID for Nils Andersson: ORCID iD orcid.org/0000-0001-8550-3843

Catalogue record

Date deposited: 12 May 2006
Last modified: 03 Dec 2019 01:56

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