Introduction / Notations

Notation used in this appendix in the demonstations :

fluxes at the faces of a -box:

volume of cells at -, -, and -points:

partial derivative notation:

is the volume element, with only that depends on time. and are the ocean domain volume and surface, respectively. No wetting/drying is allow ( ) Let and be the ocean surface and bottom, resp. ( and , where is the bottom depth).

Continuity equation with the above notation:

A quantity, is conserved when its domain averaged time change is zero, that is when:

Noting that the coordinate system used .... blah blah

equation of evolution of written as the time evolution of the vertical content of like for tracers, or momentum in flux form, the quadratic quantity is conserved when :

that is in a more compact form :

equation of evolution of written as the time evolution of like for momentum in vector invariant form, the quadratic quantity is conserved when :

that is in a more compact form :

Gurvan Madec and the NEMO Team

NEMO European Consortium2017-02-17