Articles | Volume 8, issue 6
Solid Earth, 8, 1181–1191, 2017
https://doi.org/10.5194/se-8-1181-2017
Solid Earth, 8, 1181–1191, 2017
https://doi.org/10.5194/se-8-1181-2017

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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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)
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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.