*******************
Governing Equations
*******************

**Related CPP options:**

=============== ===============================================
SOLVE3D         Solve 3D primitive equations
UV_COR          Activate Coriolis terms
UV_ADV          Activate advection terms
NBQ             Activate non-boussinesq option
CROCO_QH        Activate quasi-hydrostatique option
MRL_WCI         Activate wave-current interactions
=============== ===============================================

*Preselected options:*
::

# define SOLVE3D 
# define UV_COR 
# define UV_ADV 
# undef  NBQ
# undef  CROCO_QH
# undef  MRL_WCI

**Presentation**

By default (#undef NBQ), CROCO solves the primitive equations as in ROMS, 
from which it inherited the robustness and efficiency of its time-splitting 
implementation :cite:p:`shchepetkin_regional_2005,debreu_two-way_2012` and the 
NBQ option proposes an extension for nonhydrostatic applications. In CROCO’s 
time-splitting algorithm, the ”slow mode” is similar to ROMS internal 
(baroclinic) mode described in :cite:t:`shchepetkin_regional_2005`, whereas, 
the ”fast mode” can include, in addition to the external (barotropic) mode, 
the pseudo-acoustic mode that allows computation of the nonhydrostatic 
pressure within a non-Boussinesq approach :cite:p:`auclair_non-hydrostatic_2018`. In this 
case, the slow internal mode is also augmented by a prognostic equation of 
vertical velocity, replacing the hydrostatic equation. Another option (CROCO_QH) 
extends the PE equations to form the quasi-hydrostatic equations, relaxing the 
hypothesis of weak horizontal Coriolis force :cite:p:`marshall_hydrostatic_1997`, thus 
adding a nonhydrostatic pressure component that is solved diagnostically. Then 
another option (MRL_WCI) treats the wave-averaged equations 
:cite:p:`mcwilliams_asymptotic_2004` with wave-current interaction terms that 
are both conservative and non-conservative (needing parametrizations).


.. toctree::
   :maxdepth: 2

   model.equations.hydro
   model.equations.qh
   model.equations.wci
   model.equations.nbq