For some purposes it is advantageous to write momentum advection in eq horiz-mtm
and vert-mtm
in the (so-called) ‘vector invariant’ form:
This permits alternative numerical treatments of the non-linear terms based on their representation as a vorticity flux. Because gradients of coordinate vectors no longer appear on the rhs of vi-identity
, explicit representation of the metric terms in gu-spherical
, gv-spherical
and gw-spherical
, can be avoided: information about the geometry is contained in the areas and lengths of the volumes used to discretize the model.