Implicit viscosity in deep model

[jm-c]

There is a problem with implicit viscosity (implicitViscosity = T) when used in a deep model configuration (deepAtmosphere = T) because the current form of vertical viscous operator does not commute with surface pressure gradient in 2-D flow divergence.

An other way to view this is that with the thin-shell approximation, the vertical viscosity in the interior (excluding bottom or surface no-slip/drag friction) has no effect on the vertically integrated horizontal transport and the surface pressure gradient has no effect on the vertical shear, so that the 2 operators commute. But in the deep model, the surface pressure gradient affects the vertical shear d.u/dz (with recip_dxC * recip_deepFacC) and vertical viscosity (tendency = flux divided by deepFac2C) modifies the vertically integrated horizontal transport (factor deepFacC from dyG).

Note that the implicit viscosity looks fine to me in the anelastic formulation where the rhoFacC factor cancel nicely.