.. _doc.hydro.diag:

**Diagnoses in MARS**
#####################

Momentum equation
=================

To save the different terms of the momentum equations, add the cpp keys **-Dkey_diagdyn**.

Optional : add **-Dkey_diagdyn_details** to get the different terms of non-linear and diffusion terms. 


Description of the different terms
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The momentum equation can be written as:

                     :math:`\nu_Si=\nu_{Simax} \frac{Si}{K_{Sipsnz}+Si}`

      avec : :math:`\nu_Si`  = PLUS TARD       
             :math:`\nu_{Simax}`  = Vitesse max d'absorption de Si par Pseuso Nitzschia     (*p_psnz_vmaxSi*)
             :math:`K_{Sipsnz}` = Constante de Michaelis de Pseudo Nitzschia pour la croissance   (*p_psnz_kSi*)



The variables are saved in the output file (diag_suffix.nc) and named as follow (at u location) ::

    Coriolis term                  cor2_x : -f*v      
    Non linear advection           nlt_x_ududx : udu/dx
                                   nlt_x_vdudy : vdu/dy
                                   nlt_x_wdudz : wdu/dz
    Internal pressure gradient
                                   ipg_x : 1/rho dPi/dx
    External pressure gradient
                                   epg_x : - g d ssh / dx - 1/rho d Pa /dx
    Vertical diffusion
                                   vdif_x : dz(nz*du/dz)/dz
    Time trend
                                   dudt_x : du/dt
    


According to the sign of each terms, we must have the following balance::

    dudt_x = epg_x - cor2_x + ipg_x + (hdif_x_dnududx2 + hdif_x_dnududy2 + vdif_x) - (nlt_x_ududx + nlt_x_vdudy + nlt_x_wdudz)