doc/overview/vector_invar.rst

f67abf1ee3 Jeff*0001 Vector invariant form
                0002 ---------------------
                0003
                0004 For some purposes it is advantageous to write momentum advection in
                ** Warning **Wide character in print at /usr/local/share/lxr/source line 1030, <$git> line 6.


0005 eq :eq:`horiz-mtm` and :eq:`vert-mtm` in the (so-called) ‘vector invariant’ form:
                0006
                0007 .. math::
                0008    \frac{D\vec{\mathbf{v}}}{Dt}=\frac{\partial \vec{\mathbf{v}}}{\partial t}
0bad585a21 Navi*0009    +\left(  \nabla  \times \vec{\mathbf{v}}\right) \times \vec{\mathbf{v}} +  \nabla
f67abf1ee3 Jeff*0010    \left[ \frac{1}{2}(\vec{\mathbf{v}}\cdot \vec{\mathbf{v}})\right]
                0011    :label: vi-identity
                0012
                0013 This permits alternative numerical treatments of the non-linear terms
                0014 based on their representation as a vorticity flux. Because gradients of
                0015 coordinate vectors no longer appear on the rhs of :eq:`vi-identity`,
                0016 explicit representation of the metric terms in :eq:`gu-spherical`,
                0017 :eq:`gv-spherical` and :eq:`gw-spherical`, can be avoided: information
                0018 about the geometry is contained in the areas and lengths of the volumes
                0019 used to discretize the model.
                0020