Time evolution term (dynnxt.F90)

!-----------------------------------------------------------------------
&namdom        !   space and time domain (bathymetry, mesh, timestep)
!-----------------------------------------------------------------------
   nn_bathy    =    1      !  compute (=0) or read (=1) the bathymetry file
   rn_bathy    =    0.     !  value of the bathymetry. if (=0) bottom flat at jpkm1
   nn_closea   =    0      !  remove (=0) or keep (=1) closed seas and lakes (ORCA)
   nn_msh      =    1      !  create (=1) a mesh file or not (=0)
   rn_hmin     =   -3.     !  min depth of the ocean (>0) or min number of ocean level (<0)
   rn_e3zps_min=   20.     !  partial step thickness is set larger than the minimum of
   rn_e3zps_rat=    0.1    !  rn_e3zps_min and rn_e3zps_rat*e3t, with 0<rn_e3zps_rat<1
                           !
   rn_rdt      = 5760.     !  time step for the dynamics (and tracer if nn_acc=0)
   rn_atfp     =    0.1    !  asselin time filter parameter
   nn_acc      =    0      !  acceleration of convergence : =1      used, rdt < rdttra(k)
                                 !                          =0, not used, rdt = rdttra
   rn_rdtmin   = 28800.          !  minimum time step on tracers (used if nn_acc=1)
   rn_rdtmax   = 28800.          !  maximum time step on tracers (used if nn_acc=1)
   rn_rdth     =  800.           !  depth variation of tracer time step  (used if nn_acc=1)
   ln_crs      = .false.      !  Logical switch for coarsening module
   jphgr_msh   =       0               !  type of horizontal mesh
                                       !  = 0 curvilinear coordinate on the sphere read in coordinate.nc
                                       !  = 1 geographical mesh on the sphere with regular grid-spacing
                                       !  = 2 f-plane with regular grid-spacing
                                       !  = 3 beta-plane with regular grid-spacing
                                       !  = 4 Mercator grid with T/U point at the equator
   ppglam0     =       0.0             !  longitude of first raw and column T-point (jphgr_msh = 1)
   ppgphi0     =     -35.0             ! latitude  of first raw and column T-point (jphgr_msh = 1)
   ppe1_deg    =       1.0             !  zonal      grid-spacing (degrees)
   ppe2_deg    =       0.5             !  meridional grid-spacing (degrees)
   ppe1_m      =    5000.0             !  zonal      grid-spacing (degrees)
   ppe2_m      =    5000.0             !  meridional grid-spacing (degrees)
   ppsur       =    -4762.96143546300  !  ORCA r4, r2 and r05 coefficients
   ppa0        =      255.58049070440  ! (default coefficients)
   ppa1        =      245.58132232490  !
   ppkth       =       21.43336197938  !
   ppacr       =        3.0            !
   ppdzmin     =       10.             !  Minimum vertical spacing
   pphmax      =     5000.             !  Maximum depth
   ldbletanh   =    .TRUE.             !  Use/do not use double tanf function for vertical coordinates
   ppa2        =      100.760928500000 !  Double tanh function parameters
   ppkth2      =       48.029893720000 !
   ppacr2      =       13.000000000000 !
/

Options are defined through the namdom namelist variables. The general framework for dynamics time stepping is a leap-frog scheme, $i.e.$ a three level centred time scheme associated with an Asselin time filter (cf. Chap.3). The scheme is applied to the velocity, except when using the flux form of momentum advection (cf. §6.3) in the variable volume case (key_ vvl defined), where it has to be applied to the thickness weighted velocity (see §A.3)

$\bullet$ vector invariant form or linear free surface (ln_dynhpg_vec=true ; key_ vvl not defined):

$$\left\{ \begin{aligned}&u^{t+\rdt} = u_f^{t-\rdt} + 2\rdt \te... ...ft[ {u_f^{t-\rdt} -2u^t+u^{t+\rdt}} \right] \end{aligned} \right.$$

$\bullet$ flux form and nonlinear free surface (ln_dynhpg_vec=false ; key_ vvl defined):

$$\left\{ \begin{aligned}&\left(e_{3u} u\right)^{t+\rdt} = \left... ...^t+\left(e_{3u} u\right)^{t+\rdt}} \right] \end{aligned} \right.$$

where RHS is the right hand side of the momentum equation, the subscript $f$ denotes filtered values and $\gamma$ is the Asselin coefficient. $\gamma$ is initialized as nn_atfp (namelist parameter). Its default value is nn_atfp = $10^{-3}$. In both cases, the modified Asselin filter is not applied since perfect conservation is not an issue for the momentum equations.

Note that with the filtered free surface, the update of the after velocities is done in the dynsp_flt.F90 module, and only array swapping and Asselin filtering is done in dynnxt.F90.