Introduction to Modeling Convection in Planets and Stars by Glatzmaier Gary A

Author:Glatzmaier, Gary A.
Language: eng
Format: epub
Publisher: Princeton University Press
Published: 2013-02-04T16:00:00+00:00

so that

everywhere. Note how this is similar to how we defined the mass flux in Eq. 10.43 for a Boussinesq fluid in a cartesian box with = 1. Note also that one could use the position vector, r = , in Eq. 10.56 instead of the way we have chosen to define the poloidal and toroidal scalars with just the unit vector, . Obviously either way would work; but the equations that follow in terms of W and Z would differ due to the extra factor of r.

We then expand these scalars, W and Z, in spherical harmonics:

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