Analytical solution for viscous incompressible Stokes flow in a spherical shell

Thieulot, Cedric

doi:https://doi.org/10.5194/se-8-1181-2017

Articles | Volume 8, issue 6

Solid Earth, 8, 1181–1191, 2017

https://doi.org/10.5194/se-8-1181-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.

Solid Earth, 8, 1181–1191, 2017

https://doi.org/10.5194/se-8-1181-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 8, issue 6

Method article 24 Nov 2017

Method article | 24 Nov 2017

Analytical solution for viscous incompressible Stokes flow in a spherical shell

Cedric Thieulot

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Final revised paper (published on 24 Nov 2017)
Preprint (discussion started on 27 Jul 2017)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'review for se-2017-71', Anonymous Referee #1, 19 Aug 2017
RC2: 'Reviewer comments', Anonymous Referee #2, 30 Aug 2017
AC1: 'answer to reviewers', Cedric Thieulot, 19 Sep 2017

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Cedric THIEULOT on behalf of the Authors (19 Sep 2017) Author's response Manuscript

ED: Publish as is (26 Sep 2017) by Taras Gerya

ED: Publish as is (27 Sep 2017) by J. Huw Davies(Executive Editor)

Short summary

I present a new family of analytical flow solutions to the incompressible Stokes equation in a spherical shell. The velocity is tangential to both inner and outer boundaries, the viscosity is radial, and the solution has been designed so that the expressions for velocity, pressure, and body force are simple to implement in (geodynamics) codes. This forms the basis of a numerical benchmark for convection codes, and I have implemented it in two finite-element codes.