.. role:: cpp(code)
    :language: c++


.. _Variables:

Variable Definitions
====================

.. _`ROMS documentation`: https://www.myroms.org/wiki/Equations_of_Motion

These variable definitions are as given in the `ROMS documentation`_

+-------------------------------+--------------------------------------------+
| Space and Time Variables                                                   |
+===============================+============================================+
| :math:`t`                     | time                                       |
+-------------------------------+--------------------------------------------+
| :math:`x,y`                   | horizontal coordinates                     |
+-------------------------------+--------------------------------------------+
| :math:`z`                     | vertical coordinate                        |
+-------------------------------+--------------------------------------------+

+-------------------------------+--------------------------------------------+
| Prescribed Inputs                                                          |
+===============================+============================================+
| :math:`h(x,y)`                | bottom depth                               |
+-------------------------------+--------------------------------------------+
| :math:`g`                     | magnitude of gravity                       |
+-------------------------------+--------------------------------------------+
| :math:`f(x,y)`                | Coriolis parameter                         |
+-------------------------------+--------------------------------------------+
| :math:`\nu, \nu_\theta`       | molecular viscosity and diffusivity        |
+-------------------------------+--------------------------------------------+

+-------------------------------+--------------------------------------------+
| Prognostic Variables                                                       |
+===============================+============================================+
| :math:`\vec{v} = (u,v,w)`     | velocity vector and x-, y-, z-components   |
+-------------------------------+--------------------------------------------+
| :math:`T(x,y,z,t)`            | potential temperature                      |
+-------------------------------+--------------------------------------------+
| :math:`S(x,y,z,t)`            | salinity                                   |
+-------------------------------+--------------------------------------------+
| :math:`\zeta(x,y,t)`          | surface elevation                          |
+-------------------------------+--------------------------------------------+

+-------------------------------+--------------------------------------------+
| Diagnostic Variables                                                       |
+===============================+============================================+
| :math:`\rho_0+\rho(x,y,z,t)`  | total in situ density                      |
+-------------------------------+--------------------------------------------+
| :math:`P`                     | total pressure :math:`\approx -\rho_0 g z` |
+-------------------------------+--------------------------------------------+
| :math:`\phi(x,y,z,t)`         | dynamic pressure :math:`\phi = (P/\rho_0)` |
+-------------------------------+--------------------------------------------+
| :math:`K_m, K_C`              | vertical eddy viscosity and diffusivity    |
+-------------------------------+--------------------------------------------+

+-----------------------------------------+--------------------------------------------+
| Additional terms                                                                     |
+=========================================+============================================+
| :math:`\cal{F}_u, \cal{F}_v, \cal{F}_C` | forcing terms                              |
+-----------------------------------------+--------------------------------------------+
| :math:`\cal{D}_u, \cal{D}_v, \cal{D}_C` | diffusive terms                            |
+-----------------------------------------+--------------------------------------------+