.. _doc.basic.equations:

Scientific model description
=============================

(SORRY !! not yet ready...  )


Formalism and hypothesis
-------------------------
Geophysical fluid flows obey conservation laws for mass (:ref:`mass_conservation`), momentum (:ref:`moment_conservation`) and energy in a rotating frame (The Earth rotates towards the east). These laws can be stated in the differential form, applicable
at a fluid element.

Governing equations
+++++++++++++++++++

.. _mass_conservation:

Conservation of mass
^^^^^^^^^^^^^^^^^^^^^^




.. _moment_conservation:

Conservation of momentum
^^^^^^^^^^^^^^^^^^^^^^^^^




.. _energy_equation:

Energy equation
^^^^^^^^^^^^^^^^




Hypotheses and approximations
+++++++++++++++++++++++++++++


Geophysical equations
+++++++++++++++++++++


.. _sigma_coord:

Sigma coordinate
+++++++++++++++++
The oceans have complicated geometry and large changes in bottom depth. It is therefore
difficult to resolve the water column equally and efficiently in both shallow and deep regions of
an oceanic region simultaneously. Furthermore, since turbulent mixing plays an important role
in the circulation in the coastal ocean, a better simulation of both the upper and bottom mixed
layers is necessary. This is possible with a topographically conformal vertical coordinate system,
the so-called sigma (σ) coordinate system.