Governing Equations

1. Governing Equations#

Related CPP options:


Solve 3D primitive equations


Activate Coriolis terms


Activate advection terms


Activate non-boussinesq option


Activate quasi-hydrostatique option


Activate wave-current interactions

Preselected options:

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


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 [Shchepetkin and McWilliams, 2005, Debreu et al., 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 Shchepetkin and McWilliams [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 [Auclair et al., 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 [Marshall et al., 1997], thus adding a nonhydrostatic pressure component that is solved diagnostically. Then another option (MRL_WCI) treats the wave-averaged equations [McWilliams et al., 2004] with wave-current interaction terms that are both conservative and non-conservative (needing parametrizations).